Show that the polynomial $p_0, p_1, \ldots, p_m $ are linearly dependent.
general

Show that the polynomial $p_0, p_1, \ldots, p_m $ are linearly dependent.

Let $p_0, p_1, \ldots, p_m $ polynomials in $\mathbb{P}_m$ with the property that $p_j(1)=0\ \forall j$. Show that the polynomial $p_0, p_1, \ldots,p_m $ ...

Published: Sep 02, 2026

How do you simplify fractions that have exponents?
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How do you simplify fractions that have exponents?

I'm not sure how to simplify a fraction with a large exponent for example: $$\frac{2^{2001} \cdot 3^{2003}}{6^{2002}}$$

Published: Sep 02, 2026

Tips and tricks for proofs involving algebraic / equation manipulation
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Tips and tricks for proofs involving algebraic / equation manipulation

I recently completed a solid chunk of my first truly formal math book on Set Theory and decided to move on to Michael Spivak's Calculus (as I heard i...

Published: Sep 02, 2026

How to find the area bounded by the curve and x-axis [closed]
general

How to find the area bounded by the curve and x-axis [closed]

The text says: Determine the area bounded by the curve and $x$-axis. Could somebody solve or at least explain how I should solve these problems. $y=x^3+1....

Published: Sep 02, 2026

Finding the constant k from density function
general

Finding the constant k from density function

Wondering how to find the value of the constant k for this. I know you have to integrate, so I integrated both functions, however I'm not quite sure ...

Published: Sep 02, 2026

Solving inequalities on both sides with complex numbers
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Solving inequalities on both sides with complex numbers

I need to sketch this region $\left \{ z\in\mathbb{C}| |z-i|\leq |z-1| \right \}$. I'd like some assistance with solving this inequality because I th...

Published: Sep 02, 2026

When does the limit of a sum become an integral?
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When does the limit of a sum become an integral?

In many maths and physics texts and courses, I've been told in many cases that the limit of a sum becomes an integral, i.e. (very roughly): $$\lim_{n...

Published: Sep 02, 2026

Difference between Pure and Applied Mathematics?
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Difference between Pure and Applied Mathematics?

So, I have been looking into college courses to see what I want my major to be, and I noticed that M.I.T offers two specified types of Mathematics. Pure a...

Published: Sep 02, 2026

Why do we add a zero to dividend during long division?
general

Why do we add a zero to dividend during long division?

Suppose we want to divide 3 by 2. By Long Division we first write 1 as the first digit as the quotient, then we subtract 2 from 3, then we add a zero to t...

Published: Sep 02, 2026

Find the gradient and equation of the normal to the curve $y=x^3 + x + 5$ at the point where $x=0$
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Find the gradient and equation of the normal to the curve $y=x^3 + x + 5$ at the point where $x=0$

I was wondering if anyone can help with this question.I'm just not sure how to find the gradients and equations of these questions. If you could help...

Published: Sep 02, 2026

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