https://liberty.io/prove-the-sum-to-product-formulas-with-complex-numbers.htmlBuzz Spill Dailyen2026-09-05T08:15:22-04:00Prove the sum to product formulas with complex numbershttps://liberty.io/the-relationship-between-spectral-decomposition-eigendecomposition-and.htmlBuzz Spill Dailyen2026-09-05T08:14:36-04:00The relationship between spectral decomposition / eigendecomposition and projection operatorshttps://liberty.io/a-detail-in-the-proof-of-auslander-buchsbaum-theorem.htmlBuzz Spill Dailyen2026-09-05T07:51:32-04:00A detail in the proof of Auslander-Buchsbaum Theoremhttps://liberty.io/find-the-volume-v-of-the-described-solid-s.htmlBuzz Spill Dailyen2026-09-05T07:46:35-04:00Find the volume $V$ of the described solid $S$.https://liberty.io/antiderivative-of-sin-x-pi-3.htmlBuzz Spill Dailyen2026-09-05T07:43:23-04:00Antiderivative of $\sin(x-\pi/3)$https://liberty.io/why-is-this-series-of-square-root-of-twos-equal-pi.htmlBuzz Spill Dailyen2026-09-05T07:42:54-04:00Why is this series of square root of twos equal $\pi$?https://liberty.io/what-is-the-integral-of-a-cumulative-distribution-function.htmlBuzz Spill Dailyen2026-09-05T07:40:34-04:00What is the integral of a cumulative distribution function?https://liberty.io/log-or-antilog-tables-which-ones-are-more-useful.htmlBuzz Spill Dailyen2026-09-05T07:36:09-04:00Log or Antilog tables, which ones are more useful?https://liberty.io/solve-x-3-3x-4-0-in-real-numbers.htmlBuzz Spill Dailyen2026-09-05T07:34:49-04:00Solve $x^3 +3x -4 =0$ in Real numbershttps://liberty.io/find-the-smallest-distance-between-point-and-ellipsoid.htmlBuzz Spill Dailyen2026-09-05T07:34:48-04:00Find the smallest distance between point and ellipsoidhttps://liberty.io/definition-of-identical-in-distribution.htmlBuzz Spill Dailyen2026-09-05T07:22:03-04:00Definition of "identical in distribution"https://liberty.io/surface-area-and-volume-of-cone.htmlBuzz Spill Dailyen2026-09-05T07:16:05-04:00Surface area and volume of conehttps://liberty.io/which-is-bigger-a-googolplex-or-10-100.htmlBuzz Spill Dailyen2026-09-05T07:11:33-04:00Which is bigger: a googolplex or $10^{100!}$https://liberty.io/an-ill-conditioned-matrix.htmlBuzz Spill Dailyen2026-09-05T07:11:04-04:00An ill-conditioned matrixhttps://liberty.io/axiom-of-double-induction.htmlBuzz Spill Dailyen2026-09-05T07:10:04-04:00Axiom of Double Induction?https://liberty.io/extending-039-guess-2-3-of-the-average-039-game.htmlBuzz Spill Dailyen2026-09-05T07:04:56-04:00Extending 'Guess 2/3 of the Average' Gamehttps://liberty.io/ogf-for-partitions-of-integer-r-n-into-even-parts-less-than-or-equal-t.htmlBuzz Spill Dailyen2026-09-05T06:55:52-04:00OGF for partitions of integer r-N into even parts less than or equal to 2m (N is some integer that may depend on m).https://liberty.io/cauchy-039-s-residue-theorem-on-a-singularity-outside-a-contour.htmlBuzz Spill Dailyen2026-09-05T06:55:20-04:00Cauchy's Residue Theorem on a Singularity Outside a Contourhttps://liberty.io/minimum-number-of-attempts-to-guess-a-pin-code-given-constraints.htmlBuzz Spill Dailyen2026-09-05T06:50:42-04:00Minimum number of attempts to guess a PIN code, given constraintshttps://liberty.io/a-consequence-of-the-mean-value-theorem-for-integrals.htmlBuzz Spill Dailyen2026-09-05T06:42:21-04:00A consequence of the Mean Value Theorem for Integralshttps://liberty.io/proving-the-splitting-lemma-on-pg-147-in-at.htmlBuzz Spill Dailyen2026-09-05T06:37:55-04:00Proving the Splitting Lemma on pg.147 in AT.https://liberty.io/is-calculus-necessary-for-computer-science-student-closed.htmlBuzz Spill Dailyen2026-09-05T06:35:52-04:00Is Calculus necessary for computer science student? [closed]https://liberty.io/after-adding-10-cups-of-water-to-a-container-1-8-full-it-becomes-3-4-f.htmlBuzz Spill Dailyen2026-09-05T06:29:53-04:00After adding $10$ cups of water to a container $1/8$ full, it becomes $3/4$ full. What is the volume of the container?https://liberty.io/on-the-jacobian-determinant-for-conversion-to-cylindrical-coordinates.htmlBuzz Spill Dailyen2026-09-05T06:27:22-04:00On the Jacobian determinant for conversion to cylindrical coordinateshttps://liberty.io/what-is-the-interpretation-of-the-fundamental-theorem-of-line-integral.htmlBuzz Spill Dailyen2026-09-05T06:15:25-04:00What is the interpretation of the fundamental theorem of line integrals?https://liberty.io/describe-the-span-of-the-given-vectors-geometrically-and-algebraically.htmlBuzz Spill Dailyen2026-09-05T05:54:58-04:00Describe the span of the given vectors geometrically and algebraicallyhttps://liberty.io/precedence-between-implication-and-bi-implication.htmlBuzz Spill Dailyen2026-09-05T05:33:48-04:00Precedence between implication and bi-implicationhttps://liberty.io/what-are-the-rules-for-a-tetartoid-pentagon.htmlBuzz Spill Dailyen2026-09-05T05:28:46-04:00What are the rules for a Tetartoid pentagon?https://liberty.io/cartesian-coordinates-of-lemniscate.htmlBuzz Spill Dailyen2026-09-05T05:26:26-04:00Cartesian coordinates of lemniscatehttps://liberty.io/determining-the-area-of-a-right-triangle-perimeter-given-hypotenuse-va.htmlBuzz Spill Dailyen2026-09-05T05:26:24-04:00Determining the area of a right triangle, perimeter given, hypotenuse value given in terms of one of the legs.https://liberty.io/find-the-partial-fraction-for-frac-1-x-2-1-2-x-1.htmlBuzz Spill Dailyen2026-09-05T05:18:07-04:00Find the partial fraction for: $\frac{1}{(x^2+1)^2(x-1)}$https://liberty.io/a-box-contains-10-balls-numbered-from-1-to-10.htmlBuzz Spill Dailyen2026-09-05T05:12:31-04:00A box contains 10 balls numbered from 1 to 10https://liberty.io/why-can-039-t-you-flatten-a-sphere.htmlBuzz Spill Dailyen2026-09-05T05:11:40-04:00Why can't you flatten a sphere?https://liberty.io/extended-euclidean-algorithm-for-modular-inverse.htmlBuzz Spill Dailyen2026-09-05T05:10:37-04:00Extended Euclidean Algorithm for Modular Inversehttps://liberty.io/converting-augmented-matrix-to-reduced-row-echelon-form.htmlBuzz Spill Dailyen2026-09-05T04:57:52-04:00Converting augmented matrix to reduced row echelon formhttps://liberty.io/find-the-indicated-probability.htmlBuzz Spill Dailyen2026-09-05T04:54:31-04:00Find the Indicated Probabilityhttps://liberty.io/find-the-arclength-of-the-curve-defined-by-r-t-i-9t-2j-t-3k-for-0-leq-.htmlBuzz Spill Dailyen2026-09-05T04:54:23-04:00Find the arclength of the curve defined by $r(t)=i+9t^2j+t^3k$ for $0 \leq t \leq \sqrt28$.https://liberty.io/classifying-map.htmlBuzz Spill Dailyen2026-09-05T04:48:51-04:00Classifying maphttps://liberty.io/sum-of-multiplication-of-two-binomial-coefficients.htmlBuzz Spill Dailyen2026-09-05T04:47:35-04:00sum of multiplication of two binomial coefficientshttps://liberty.io/why-do-divisions-like-1-98-and-1-998-give-us-numbers-continuously-bein.htmlBuzz Spill Dailyen2026-09-05T04:42:17-04:00Why do divisions like 1/98 and 1/998 give us numbers continuously being multiplied by two each time in decimal form?https://liberty.io/positive-and-negative-complex-numbers.htmlBuzz Spill Dailyen2026-09-05T04:40:15-04:00Positive and negative complex numbers?https://liberty.io/relative-interpretations-alla-kunen.htmlBuzz Spill Dailyen2026-09-05T04:38:14-04:00Relative Interpretations alla Kunenhttps://liberty.io/formula-for-the-sequence-1-1-2-2-3-3-closed.htmlBuzz Spill Dailyen2026-09-05T04:38:06-04:00Formula for the sequence 1 1 2 2 3 3 [closed]https://liberty.io/understanding-the-earth-mover-s-distance-emd-from-the-matlab.htmlBuzz Spill Dailyen2026-09-05T04:35:30-04:00understanding the Earth Mover’s Distance (EMD) from the MATLABhttps://liberty.io/is-there-any-significant-consequence-if-p-does-not-equal-np-complete.htmlBuzz Spill Dailyen2026-09-05T04:30:32-04:00Is there any significant consequence if P does not equal NP-complete?https://liberty.io/calculating-inverse-trig-expressions-like-cos-arctan-2.htmlBuzz Spill Dailyen2026-09-05T04:25:31-04:00Calculating inverse trig expressions like cos(arctan -2)https://liberty.io/proof-of-schur-039-s-lemma.htmlBuzz Spill Dailyen2026-09-05T04:24:35-04:00Proof of Schur's lemmahttps://liberty.io/is-7-5040-the-largest-highly-composite-factorial.htmlBuzz Spill Dailyen2026-09-05T04:22:49-04:00Is $\ 7!=5040\ $ the largest highly composite factorial?https://liberty.io/extremas-using-lagrange-or-other-methods-with-exponential-functions.htmlBuzz Spill Dailyen2026-09-05T04:18:23-04:00Extremas using Lagrange or other methods with exponential functionshttps://liberty.io/giving-two-equal-line-segments-ac-and-bd-so-that-they-bisect-each-othe.htmlBuzz Spill Dailyen2026-09-05T04:15:46-04:00Giving two equal line segments AC and BD so that they bisect each other at E. Prove that quadrilateral ABCD is a Rectangle.https://liberty.io/complex-space-why-unit-disc.htmlBuzz Spill Dailyen2026-09-05T04:11:04-04:00Complex Space : Why unit disc?https://liberty.io/complete-graph-k-n-can-be-expressed-as-the-union-of-k-bipartite-graphs.htmlBuzz Spill Dailyen2026-09-05T03:59:08-04:00Complete graph $K_n$ can be expressed as the union of $k$ bipartite graphs if and only if $n \leq 2^ k$ (proof understanding as in D.B West)https://liberty.io/simplest-way-to-count-distinct-combinations-2.htmlBuzz Spill Dailyen2026-09-05T03:51:08-04:00Simplest way to count distinct combinations #2https://liberty.io/making-sense-of-a-cross-product-of-three-vectors.htmlBuzz Spill Dailyen2026-09-05T03:47:49-04:00Making sense of a cross product of three vectorshttps://liberty.io/why-do-we-disregard-the-remainder-while-finding-an-oblique-asymptote.htmlBuzz Spill Dailyen2026-09-05T03:25:22-04:00Why do we disregard the remainder while finding an oblique asymptote?https://liberty.io/does-the-definition-of-the-angle-between-two-vectors-require-that-they.htmlBuzz Spill Dailyen2026-09-05T03:22:13-04:00Does the definition of the angle between two vectors require that they have the same "origin"?https://liberty.io/quotient-groups-of-d10.htmlBuzz Spill Dailyen2026-09-05T03:20:08-04:00Quotient groups of D10https://liberty.io/definition-of-measurability.htmlBuzz Spill Dailyen2026-09-05T03:10:53-04:00Definition of measurabilityhttps://liberty.io/the-volume-of-a-torus.htmlBuzz Spill Dailyen2026-09-05T03:07:51-04:00The volume of a Torushttps://liberty.io/what-does-ir-mean-in-linear-algebra.htmlBuzz Spill Dailyen2026-09-05T03:02:51-04:00What does "IR" mean in linear algebra?https://liberty.io/determine-whether-this-statement-is-true-or-false-forall-x-in-z-exists.htmlBuzz Spill Dailyen2026-09-05T02:50:06-04:00Determine whether this statement is true or false $\forall x \in {Z}, \exists y , z \in {Z} [x = 5y + 7z] $https://liberty.io/why-is-it-important-for-a-matrix-to-be-square.htmlBuzz Spill Dailyen2026-09-05T02:44:01-04:00Why is it important for a matrix to be square?https://liberty.io/constructing-a-square-from-the-difference-of-diagonal-and-side.htmlBuzz Spill Dailyen2026-09-05T02:41:29-04:00Constructing a square from the difference of diagonal and sidehttps://liberty.io/what-are-the-differences-between-rings-groups-and-fields.htmlBuzz Spill Dailyen2026-09-05T02:37:39-04:00What are the differences between rings, groups, and fields?https://liberty.io/turn-partial-differential-equation-into-ordinary-differential-equation.htmlBuzz Spill Dailyen2026-09-05T02:37:00-04:00Turn Partial Differential Equation into Ordinary Differential Equationhttps://liberty.io/square-root-of-sqrt-1-4-sqrt-3-i.htmlBuzz Spill Dailyen2026-09-05T02:30:41-04:00Square root of $\sqrt{1-4\sqrt{3}i}$https://liberty.io/how-to-use-double-angle-identities-to-find-length-039-d-039.htmlBuzz Spill Dailyen2026-09-05T02:17:25-04:00How to use double angle identities to find length 'd'?https://liberty.io/how-to-prove-distance-from-foci-on-an-ellipse-is-equal-to-twice-the-se.htmlBuzz Spill Dailyen2026-09-05T02:17:20-04:00How to prove distance from foci on an ellipse is equal to twice the semi-major axis (for specific ellipse)https://liberty.io/linear-approximation-with-two-variables.htmlBuzz Spill Dailyen2026-09-05T02:09:52-04:00Linear approximation with two variableshttps://liberty.io/definition-of-an-angle-vs-measurement-of-an-angle.htmlBuzz Spill Dailyen2026-09-05T02:01:11-04:00Definition of an angle vs measurement of an anglehttps://liberty.io/how-could-a-square-root-of-fraction-have-a-negative-root.htmlBuzz Spill Dailyen2026-09-05T02:00:56-04:00How could a square root of fraction have a negative root?https://liberty.io/piecewise-function-plot-in-matlab.htmlBuzz Spill Dailyen2026-09-05T01:59:36-04:00Piecewise function plot in Matlabhttps://liberty.io/how-to-solve-this-limit-lim-limits-x-to0-frac-1-x-1-x-e-x-duplicate.htmlBuzz Spill Dailyen2026-09-05T01:50:26-04:00How to solve this limit: $\lim\limits_{x\to0}\frac{(1+x)^{1/x}-e}x$? [duplicate]https://liberty.io/even-and-odd-cubic-polynomials.htmlBuzz Spill Dailyen2026-09-05T01:32:58-04:00even and odd cubic polynomialshttps://liberty.io/volume-of-a-parabola-rotated-around-a-line.htmlBuzz Spill Dailyen2026-09-05T01:32:13-04:00Volume of a Parabola Rotated Around a Linehttps://liberty.io/evaluate-the-indefinite-integral-int-1-x-2-3-2-dx.htmlBuzz Spill Dailyen2026-09-05T01:26:57-04:00Evaluate the indefinite integral $\int {(1-x^2)^{-3/2}}dx$https://liberty.io/riesz-functional-calculus-vs-holomorphic-functional-calculus.htmlBuzz Spill Dailyen2026-09-05T01:26:56-04:00Riesz Functional Calculus vs. Holomorphic Functional Calculushttps://liberty.io/find-the-matrix-s-of-stretch-by-a-factor-of-3.htmlBuzz Spill Dailyen2026-09-05T01:21:04-04:00Find the matrix $S$ of stretch by a factor of $3$.https://liberty.io/deriving-the-midpoint-formula-in-3d-using-the-distance-formula.htmlBuzz Spill Dailyen2026-09-05T01:17:16-04:00Deriving the midpoint formula in 3D using the distance formulahttps://liberty.io/cosine-and-sine-of-the-angle-multiplied-by-a-scalar.htmlBuzz Spill Dailyen2026-09-05T01:02:29-04:00cosine and sine of the angle multiplied by a scalarhttps://liberty.io/what-039-s-the-formula-to-solve-summation-of-logarithms.htmlBuzz Spill Dailyen2026-09-05T00:59:25-04:00What's the formula to solve summation of logarithms?https://liberty.io/how-to-get-the-exact-value-of-sin-x-if-sin-2x-frac-24-25.htmlBuzz Spill Dailyen2026-09-05T00:46:46-04:00How to get the exact value of $\sin(x)$ if $\sin(2x) = \frac{24}{25}$https://liberty.io/matrix-for-reflection-about-the-line-y-tan-theta-x.htmlBuzz Spill Dailyen2026-09-05T00:42:14-04:00Matrix for reflection about the line $y = \tan (\theta) \, x$https://liberty.io/some-integral-representations-of-the-euler-mascheroni-constant.htmlBuzz Spill Dailyen2026-09-05T00:33:42-04:00Some integral representations of the Euler–Mascheroni constanthttps://liberty.io/proving-a-cup-b-cap-c-a-cup-b-cap-a-cup-c.htmlBuzz Spill Dailyen2026-09-05T00:25:52-04:00Proving $A \cup (B \cap C) = (A \cup B) \cap (A \cup C)$.https://liberty.io/90-degree-counter-clockwise-rotation-around-a-point.htmlBuzz Spill Dailyen2026-09-05T00:23:49-04:0090 degree counter-clockwise rotation around a pointhttps://liberty.io/the-thinking-behind-4-times-5-is-12-and-4-times-6-is-13-and-4-times-7-.htmlBuzz Spill Dailyen2026-09-05T00:20:25-04:00The thinking behind "4 times 5 is 12, and 4 times 6 is 13, and 4 times 7 is-oh dear! I shall never get to 20 at that rate!" from Alice in Wonderland?https://liberty.io/solve-the-following-differential-equation-y-frac-dx-dy-x-2y-2-with-the.htmlBuzz Spill Dailyen2026-09-05T00:20:18-04:00Solve the following differential equation: $y\frac{dx}{dy}-x=2y^2$, with the initial condition $y(1)=5$.https://liberty.io/methods-of-enumeration-stars-and-bars.htmlBuzz Spill Dailyen2026-09-05T00:20:00-04:00Methods of Enumeration - Stars and Barshttps://liberty.io/syllogism-in-mathematics.htmlBuzz Spill Dailyen2026-09-05T00:11:40-04:00syllogism in mathematicshttps://liberty.io/finding-anchor-and-reference-point-of-a-cube-root-function.htmlBuzz Spill Dailyen2026-09-05T00:02:53-04:00Finding Anchor and Reference Point of a Cube Root Function.https://liberty.io/evaluate-the-following-definite-integrals-using-the-fundamental-theore.htmlBuzz Spill Dailyen2026-09-04T23:53:44-04:00Evaluate the following definite integrals using the Fundamental Theorem of Calculushttps://liberty.io/find-the-solution-of-the-given-initial-value-problem-differential-equa.htmlBuzz Spill Dailyen2026-09-04T23:51:26-04:00Find the solution of the given initial value problem (differential equations)https://liberty.io/what-is-the-difference-between-singular-matrices-and-degenerate-matric.htmlBuzz Spill Dailyen2026-09-04T23:49:57-04:00What is the difference between singular matrices and degenerate matrices?https://liberty.io/notation-for-a-vector-with-constant-equal-components-of-arbitrary-dime.htmlBuzz Spill Dailyen2026-09-04T23:47:52-04:00Notation for a vector with constant equal components of arbitrary dimensionhttps://liberty.io/what-is-the-difference-between-projected-gradient-descent-and-ordinary.htmlBuzz Spill Dailyen2026-09-04T23:36:59-04:00What is the difference between projected gradient descent and ordinary gradient descent?https://liberty.io/total-graph-definition.htmlBuzz Spill Dailyen2026-09-04T23:33:32-04:00Total graph definitionhttps://liberty.io/proof-of-the-fundamental-theorem-of-line-integrals.htmlBuzz Spill Dailyen2026-09-04T23:27:30-04:00Proof of the fundamental theorem of line integralshttps://liberty.io/what-does-it-mean-that-multiplication-and-division-have-the-same-prece.htmlBuzz Spill Dailyen2026-09-04T23:25:08-04:00What does it mean that multiplication and division have the same precedence?https://liberty.io/plane-parallel-to-the-base-of-a-triangular-pyramid.htmlBuzz Spill Dailyen2026-09-04T23:20:49-04:00Plane parallel to the base of a triangular pyramid