https://liberty.io/rotating-rectangle-90-degrees-clockwise.htmlBuzz Spill Dailyen2026-08-31T20:40:05-04:00Rotating rectangle 90 degrees clockwisehttps://liberty.io/let-t-x-2y-xy-3-2-where-x-r-cos-theta-y-r-sin-theta-find-frac-partial-.htmlBuzz Spill Dailyen2026-08-31T20:36:56-04:00Let $T = x^2y-xy^3+2$ ; where $x = r\cos\theta, y=r\sin\theta$. Find $\frac{\partial T}{\partial r}$ and $\frac{\partial T}{\partial \theta}$https://liberty.io/how-to-integrate-int-x-n-e-x-dx.htmlBuzz Spill Dailyen2026-08-31T20:35:32-04:00How to integrate $ \int x^n e^x dx$?https://liberty.io/prob-15-chap-6-in-baby-rudin-if-f-is-a-real-continuously-differentiabl.htmlBuzz Spill Dailyen2026-08-31T20:33:14-04:00Prob. 15, Chap. 6, in Baby Rudin: If $f$ is a real, continuously differentiable function on $[a, b]$, . . .https://liberty.io/linear-transformation-from-r-3-to-r-2.htmlBuzz Spill Dailyen2026-08-31T20:28:33-04:00Linear transformation from $R^3$ to $R^2$.https://liberty.io/infinity-plus-infinity.htmlBuzz Spill Dailyen2026-08-31T20:20:12-04:00Infinity plus Infinityhttps://liberty.io/upper-bound-on-the-number-of-edges-in-the-farthest-point-voronoi-diagr.htmlBuzz Spill Dailyen2026-08-31T20:19:03-04:00Upper-bound on the number of edges in the farthest-point voronoi diagramhttps://liberty.io/diagonalizing-the-matrix-if-possible.htmlBuzz Spill Dailyen2026-08-31T20:17:20-04:00Diagonalizing the matrix (if possible)https://liberty.io/calculating-surface-area-of-a-sphere-with-cylindrical-coordinates.htmlBuzz Spill Dailyen2026-08-31T20:15:48-04:00Calculating surface area of a sphere with cylindrical coordinateshttps://liberty.io/does-zero-divide-zero.htmlBuzz Spill Dailyen2026-08-31T20:14:41-04:00Does zero divide zerohttps://liberty.io/how-is-ln-pronounced-by-english-speakers.htmlBuzz Spill Dailyen2026-08-31T20:04:42-04:00How is $\ln$ pronounced by English speakers?https://liberty.io/length-of-a-parabolic-curve.htmlBuzz Spill Dailyen2026-08-31T20:00:50-04:00Length of a Parabolic Curvehttps://liberty.io/epsilon-delta-derivative-proof-of-x-n.htmlBuzz Spill Dailyen2026-08-31T19:50:15-04:00Epsilon-delta derivative proof of $x^n$https://liberty.io/average-path-length-of-unconnected-graphs.htmlBuzz Spill Dailyen2026-08-31T19:48:24-04:00Average path length of unconnected graphshttps://liberty.io/cos-2-alpha-cos-2-beta-cos-2-gamma-1-duplicate.htmlBuzz Spill Dailyen2026-08-31T19:42:28-04:00$\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma =1$ [duplicate]https://liberty.io/definition-of-an-affine-subspace.htmlBuzz Spill Dailyen2026-08-31T19:40:02-04:00Definition of an affine subspacehttps://liberty.io/integral-int-0-1-frac-arctan-x-x-2-x-1-dx.htmlBuzz Spill Dailyen2026-08-31T19:29:03-04:00Integral $\int_0^1 \frac{\arctan x}{x^2-x-1}dx$https://liberty.io/contour-integral-for-x-3-e-x-1.htmlBuzz Spill Dailyen2026-08-31T19:13:01-04:00Contour integral for $x^3/(e^x-1)$?https://liberty.io/find-diagonal-of-inverse-matrix.htmlBuzz Spill Dailyen2026-08-31T19:12:07-04:00Find diagonal of inverse matrixhttps://liberty.io/how-to-simplify-log-base-2-and-log-base-4.htmlBuzz Spill Dailyen2026-08-31T19:04:55-04:00how to simplify log base 2 and log base 4https://liberty.io/simplify-sin-1-tan-x.htmlBuzz Spill Dailyen2026-08-31T18:50:01-04:00simplify $\sin^{-1}(\tan x)$https://liberty.io/construct-a-bijective-map-and-prove-it-is-bijective.htmlBuzz Spill Dailyen2026-08-31T18:45:45-04:00Construct a bijective map and prove it is bijectivehttps://liberty.io/integral-int-limits-0-pi-sin-x-cos-x-dx.htmlBuzz Spill Dailyen2026-08-31T18:32:37-04:00Integral $\int \limits _0 ^\pi |\sin x + \cos x|\; dx$https://liberty.io/finding-general-formula-for-a-recursion-function.htmlBuzz Spill Dailyen2026-08-31T18:27:07-04:00Finding general formula for a recursion functionhttps://liberty.io/proving-the-fundamental-period-of-tangent.htmlBuzz Spill Dailyen2026-08-31T18:20:27-04:00Proving the fundamental period of tangenthttps://liberty.io/probability-of-drawing-5-cards-from-a-deck-of-52-that-will-have-the-sa.htmlBuzz Spill Dailyen2026-08-31T18:13:17-04:00Probability of drawing 5 cards from a deck of 52 that will have the same suit?https://liberty.io/prove-convergent-sequences-are-bounded.htmlBuzz Spill Dailyen2026-08-31T18:00:45-04:00Prove: Convergent sequences are boundedhttps://liberty.io/isomorphism-classes-of-abelian-groups-of-certain-order.htmlBuzz Spill Dailyen2026-08-31T18:00:02-04:00Isomorphism classes of abelian groups of certain orderhttps://liberty.io/independence-of-a-random-variable-x-from-itself.htmlBuzz Spill Dailyen2026-08-31T17:44:58-04:00Independence of a random variable $X$ from itselfhttps://liberty.io/what-is-the-difference-between-p-a-b-and-p-a-b.htmlBuzz Spill Dailyen2026-08-31T17:42:39-04:00What is the difference between $p(a,b)$ and $p(a|b)$?https://liberty.io/asymptotic-approximation-of-the-arctangent.htmlBuzz Spill Dailyen2026-08-31T17:39:52-04:00Asymptotic approximation of the arctangent?https://liberty.io/use-cylindrical-coordinates-to-find-the-volume-of-a-solid.htmlBuzz Spill Dailyen2026-08-31T17:38:13-04:00Use cylindrical coordinates to find the volume of a solid.https://liberty.io/definition-of-maximal-and-minimal-duplicate.htmlBuzz Spill Dailyen2026-08-31T17:36:44-04:00Definition of “maximal” and “minimal” [duplicate]https://liberty.io/difference-between-basis-and-subbasis-in-a-topology.htmlBuzz Spill Dailyen2026-08-31T17:29:02-04:00Difference between basis and subbasis in a topology?https://liberty.io/definition-of-an-induced-matrix-norm.htmlBuzz Spill Dailyen2026-08-31T17:27:02-04:00Definition of an induced matrix norm.https://liberty.io/polynomial-whose-roots-adjoin-to-a-field-mathbb-q-sqrt6-to-give-an-ext.htmlBuzz Spill Dailyen2026-08-31T17:26:20-04:00Polynomial whose roots adjoin to a field $\mathbb Q(\sqrt6)$ to give an extension field $\mathbb Q(\sqrt2,\sqrt3)$https://liberty.io/finding-eccentricity-from-the-rotating-ellipse-formula.htmlBuzz Spill Dailyen2026-08-31T17:19:43-04:00Finding Eccentricity from the rotating ellipse formulahttps://liberty.io/proof-of-arctan-2-pi-2-arctan-1-2.htmlBuzz Spill Dailyen2026-08-31T16:58:51-04:00Proof of $\arctan{2} = \pi/2 -\arctan{1/2}$https://liberty.io/hyperbolic-curve-and-hyperbola.htmlBuzz Spill Dailyen2026-08-31T16:57:47-04:00Hyperbolic curve and hyperbola?https://liberty.io/solving-right-triangle-given-two-sides.htmlBuzz Spill Dailyen2026-08-31T16:54:44-04:00Solving Right Triangle Given Two Sideshttps://liberty.io/what-is-the-exact-definition-of-a-reflexive-relation.htmlBuzz Spill Dailyen2026-08-31T16:48:33-04:00What is the exact definition of a reflexive relation?https://liberty.io/determine-the-signs-of-the-partial-derivatives-for-the-function-f-whos.htmlBuzz Spill Dailyen2026-08-31T16:38:19-04:00Determine the signs of the partial derivatives for the function f whose graph is shown below.https://liberty.io/does-det-a-b-det-a-det-b-hold.htmlBuzz Spill Dailyen2026-08-31T16:37:19-04:00Does $\det(A + B) = \det(A) + \det(B)$ hold?https://liberty.io/find-angle-in-triangle-with-incenter.htmlBuzz Spill Dailyen2026-08-31T16:33:22-04:00Find angle in triangle with incenterhttps://liberty.io/how-to-prove-sin-x-sin-y-2-sin-left-frac-x-y-2-right-cos-left-frac-x-y.htmlBuzz Spill Dailyen2026-08-31T16:30:46-04:00How to prove $\sin (x)+ \sin(y) = 2 \sin \left(\frac{x+y}{2}\right) \cos\left(\frac{x-y}{2}\right)$ using addition theorems?https://liberty.io/multivariable-calculus-hard-problems-with-solutions.htmlBuzz Spill Dailyen2026-08-31T16:23:44-04:00Multivariable calculus: hard problems with solutionshttps://liberty.io/does-the-existence-of-orthocenter-proof-also-work-for-obtuse-triangles.htmlBuzz Spill Dailyen2026-08-31T16:05:19-04:00Does the "existence of orthocenter" proof also work for obtuse triangles?https://liberty.io/proving-the-klein-4-group-is-abelian.htmlBuzz Spill Dailyen2026-08-31T15:58:18-04:00proving the Klein 4 group is abelianhttps://liberty.io/simple-diffy-q-problem.htmlBuzz Spill Dailyen2026-08-31T15:58:17-04:00Simple Diffy-Q problemhttps://liberty.io/general-solution-for-a-nonhomogeneous-differential-equation.htmlBuzz Spill Dailyen2026-08-31T15:57:41-04:00General solution for a nonhomogeneous differential equationhttps://liberty.io/can-someone-explain-the-concept-of-fundamental-domain-to-me.htmlBuzz Spill Dailyen2026-08-31T15:51:25-04:00Can someone explain the concept of Fundamental Domain to me?https://liberty.io/why-are-there-3-solutions-in-this-trigonometric-equation-sin-theta-0.htmlBuzz Spill Dailyen2026-08-31T15:47:55-04:00Why are there 3 solutions in this trigonometric equation $sin\theta = 0$https://liberty.io/the-significance-of-linear-approximation.htmlBuzz Spill Dailyen2026-08-31T15:47:30-04:00The Significance of Linear Approximationhttps://liberty.io/constant-of-integration-of-the-integrating-factor.htmlBuzz Spill Dailyen2026-08-31T15:44:02-04:00Constant of Integration of the Integrating Factorhttps://liberty.io/how-to-compute-dottie-number-accurately.htmlBuzz Spill Dailyen2026-08-31T15:43:19-04:00How to compute Dottie number accurately?https://liberty.io/order-of-elements-in-bbb-z-24.htmlBuzz Spill Dailyen2026-08-31T15:31:33-04:00Order of elements in $\Bbb Z_{24}$https://liberty.io/finding-domain-of-a-function-with-a-natural-logarithm-at-the-denominat.htmlBuzz Spill Dailyen2026-08-31T15:29:37-04:00Finding Domain of a Function with a natural logarithm at the denominator of the fractionhttps://liberty.io/cardinality-of-the-set-of-all-prime-factors-of-120-closed.htmlBuzz Spill Dailyen2026-08-31T15:28:20-04:00cardinality of the set of all prime factors of 120 [closed]https://liberty.io/the-wald-test-with-poisson-distribution.htmlBuzz Spill Dailyen2026-08-31T15:11:26-04:00The Wald test with Poisson distributionhttps://liberty.io/find-the-residues-of-frac-1-sin-pi-z-closed.htmlBuzz Spill Dailyen2026-08-31T15:06:52-04:00Find the residues of $\frac{1}{\sin \pi z}$ [closed]https://liberty.io/probability-of-winning-a-game-of-craps.htmlBuzz Spill Dailyen2026-08-31T15:05:09-04:00Probability of winning a game of crapshttps://liberty.io/converting-an-equation-from-cartesian-to-polar-form.htmlBuzz Spill Dailyen2026-08-31T14:51:09-04:00Converting an equation from Cartesian to Polar form?https://liberty.io/how-to-evaluate-the-complex-logarithms-log-i-and-log-3-4i.htmlBuzz Spill Dailyen2026-08-31T14:47:23-04:00How to evaluate the complex logarithms $\log(i)$ and $\log(3+4i)$?https://liberty.io/non-isosceles-triangles-with-vertices-in-a-20-sided-regular-polygon.htmlBuzz Spill Dailyen2026-08-31T14:46:15-04:00non-isosceles triangles with vertices in a 20-sided regular polygon.https://liberty.io/random-sample-vs-simple-random-sample.htmlBuzz Spill Dailyen2026-08-31T14:42:59-04:00Random Sample vs Simple Random Samplehttps://liberty.io/how-do-find-if-a-relation-is-a-function-algebraically.htmlBuzz Spill Dailyen2026-08-31T14:42:48-04:00How do find if a relation is a function algebraicallyhttps://liberty.io/what-does-smooth-curve-mean.htmlBuzz Spill Dailyen2026-08-31T14:42:02-04:00What does smooth curve mean?https://liberty.io/linear-algebra-understanding-the-column-picture.htmlBuzz Spill Dailyen2026-08-31T14:38:45-04:00Linear Algebra - understanding the column picturehttps://liberty.io/what-is-the-angle-of-b.htmlBuzz Spill Dailyen2026-08-31T14:31:39-04:00What is the angle of b?https://liberty.io/the-precise-meaning-of-the-limit-that-defines-the-integral.htmlBuzz Spill Dailyen2026-08-31T14:26:13-04:00The precise meaning of the limit that defines the integralhttps://liberty.io/what-is-the-contrapositive-of-the-definition-of-onto.htmlBuzz Spill Dailyen2026-08-31T14:04:42-04:00What is the contrapositive of the definition of onto?https://liberty.io/prove-that-triangle-amc-is-an-isosceles-right-triangle.htmlBuzz Spill Dailyen2026-08-31T13:57:38-04:00Prove that $\triangle AMC$ is an isosceles right trianglehttps://liberty.io/limit-as-x-goes-to-infinity-of-absolute-value.htmlBuzz Spill Dailyen2026-08-31T13:46:24-04:00Limit as x goes to infinity of absolute valuehttps://liberty.io/an-example-of-an-operation-in-ordinary-arithmetic-that-is-idempotent.htmlBuzz Spill Dailyen2026-08-31T13:41:19-04:00An example of an operation in ordinary arithmetic that is idempotenthttps://liberty.io/solution-of-a-dirichlet-problem-on-the-unit-disk.htmlBuzz Spill Dailyen2026-08-31T13:40:15-04:00Solution of a Dirichlet problem on the unit diskhttps://liberty.io/what-is-sin-pi-2-iln2.htmlBuzz Spill Dailyen2026-08-31T13:37:13-04:00What is $sin(\pi/2 +iln2)$https://liberty.io/understanding-field-extension.htmlBuzz Spill Dailyen2026-08-31T13:36:15-04:00Understanding field extensionhttps://liberty.io/pendulum-with-oscillating-fulcrum-equations-of-motion.htmlBuzz Spill Dailyen2026-08-31T13:32:30-04:00Pendulum with oscillating Fulcrum | Equations of Motionhttps://liberty.io/intuition-for-polynomial-long-division.htmlBuzz Spill Dailyen2026-08-31T13:22:18-04:00Intuition for polynomial long divisionhttps://liberty.io/length-of-tangent-from-one-circle-to-another.htmlBuzz Spill Dailyen2026-08-31T13:21:03-04:00Length of tangent from one circle to anotherhttps://liberty.io/proof-of-and-requirements-for-the-reverse-of-jensen-039-s-inequality-f.htmlBuzz Spill Dailyen2026-08-31T13:16:11-04:00Proof of, and requirements for, the reverse of Jensen's Inequality for concave functionshttps://liberty.io/karnaugh-map-and-circuit-of-a-full-adder.htmlBuzz Spill Dailyen2026-08-31T13:15:11-04:00Karnaugh map and Circuit of a full adderhttps://liberty.io/proving-that-that-f-x-cos-x-sin-tan-x-if-x-neq-pi-2-is-continuous.htmlBuzz Spill Dailyen2026-08-31T13:05:23-04:00Proving that that $ f(x) = \cos(x) \sin(\tan(x)) $ if $ x \neq \pi / 2 $ is continuoushttps://liberty.io/linear-algebra-dimension-theorem.htmlBuzz Spill Dailyen2026-08-31T13:04:35-04:00Linear algebra - Dimension theorem.https://liberty.io/if-3-gon-and-5-gon-are-constructible-show-that-15-gon-is-too.htmlBuzz Spill Dailyen2026-08-31T13:04:20-04:00If $3-$gon and $5-$gon are constructible, show that $15-$gon is too.https://liberty.io/inner-product-space-parallelogram-law.htmlBuzz Spill Dailyen2026-08-31T13:00:17-04:00Inner product space parallelogram law?https://liberty.io/can-i-get-multivariable-taylor-series-expansion-on-wolfram-alpha-or-ma.htmlBuzz Spill Dailyen2026-08-31T12:46:58-04:00Can I get multivariable taylor series expansion on wolfram alpha or matlab?https://liberty.io/what-is-a-physical-dimension-in-the-sense-of-dimensional-analysis.htmlBuzz Spill Dailyen2026-08-31T12:44:38-04:00What is a physical “dimension” - in the sense of “dimensional” analysis?https://liberty.io/recursively-defined-set-subset-proof.htmlBuzz Spill Dailyen2026-08-31T12:38:24-04:00Recursively defined set subset proofhttps://liberty.io/proving-the-complementation-law-for-sets.htmlBuzz Spill Dailyen2026-08-31T12:33:09-04:00Proving the Complementation Law for setshttps://liberty.io/the-graph-has-10-vertices-and-47-edges-closed.htmlBuzz Spill Dailyen2026-08-31T12:32:24-04:00The graph has 10 vertices and 47 edges. [closed]https://liberty.io/logarithmic-differentiation-of-some-functions.htmlBuzz Spill Dailyen2026-08-31T12:32:22-04:00Logarithmic differentiation of some functionshttps://liberty.io/nested-summation-and-product-notation-of-two-expressions.htmlBuzz Spill Dailyen2026-08-31T11:59:15-04:00Nested summation and product notation of two expressionshttps://liberty.io/proving-rolle-039-s-theorem.htmlBuzz Spill Dailyen2026-08-31T11:59:04-04:00Proving Rolle's Theoremhttps://liberty.io/proof-of-an-abstract-bayes-039-theorem.htmlBuzz Spill Dailyen2026-08-31T11:53:41-04:00Proof of an Abstract Bayes' Theoremhttps://liberty.io/solving-a-integro-differential-equation.htmlBuzz Spill Dailyen2026-08-31T11:49:33-04:00Solving a integro-differential equationhttps://liberty.io/an-easy-example-of-a-non-constructive-proof-without-an-obvious-fix.htmlBuzz Spill Dailyen2026-08-31T11:44:25-04:00An easy example of a non-constructive proof without an obvious "fix"?https://liberty.io/understanding-euclid-039-s-proof-that-the-number-of-primes-is-infinite.htmlBuzz Spill Dailyen2026-08-31T11:39:48-04:00Understanding Euclid's proof that the number of primes is infinite. [duplicate]https://liberty.io/is-there-any-symbol-for-undefined-duplicate.htmlBuzz Spill Dailyen2026-08-31T11:21:51-04:00Is there any symbol for "undefined"? [duplicate]https://liberty.io/write-the-following-in-the-form-of-ax-b.htmlBuzz Spill Dailyen2026-08-31T11:20:47-04:00Write the following in the form of AX = B