Recent questions tagged theorem

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Describe the Residue Theorem and its applications.
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State and explain Cauchy's Integral Theorem.
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What is the Intermediate Value Theorem (IVT)?
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What is the Bolzano-Weierstrass theorem?
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Prove Bezout's Theorem for Plane Curves
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Suppose that $f$ is an entire function, and$$ | f(z) | \leq A + B|z|^k$$for all $z$, where $A, B, k$ are positive real numbers. Prove that $f$ must be polynomial.
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Let $\{ x_i \}_{i=1}^n \subset \mathbb{R}^D$. Define $F: \mathbb{R}^D \to [0,\infty)$ via:$$ F(y) = \sum_{i=1}^n \Vert x_i - y \Vert_2^2$$Prove that $F$ attains a minimum...
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Find (a) all horizontal and (b) all vertical asymptotes of the graph\[y=\frac{|x| \sqrt{4 x^{4}+6 x^{2}+4}}{(2 x-1)^{2}(x+1)}\]
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In circle O, diameter AB is perpendicular to chord CD at E. If AO = 10 and EB = 4, what is CD?
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What is Fermat's Little Theorem?
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What is the main result of the Chinese Remainder Theorem?
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What is the fundamental theorem of arithmetic?
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State the equipartition theorem
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Prove the mean value theorem by first reducing to the case \( u(a)=u(b)=0 \) and then using the fact that \( u(x) \) must take on a maximum or minimum value for some poin...
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Find the vertical and horizontal asymptotes of the graph of the function \( f(x)=\sqrt{x+1}-\sqrt{x} \).
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Find the vertical and horizontal asymptotes of the graph of the function \( f(x)=(2 x+3) / \sqrt{x^{2}-2 x-3} \).
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Find any vertical and horizontal asymptotes of the graph of the function \( f(x)=(4 x-5) /(3 x+2) \).
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State Green's theorem in the plane.
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State Gauss' Theorem
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Is the angle between the tangent and the chord equal to the angle in the alternate segment?
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What is the Fermat's Last Theorem?
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What is the Pythagoras's Theorem for?
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Regarding polynomials – What does the remainder theorem consist of?
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What does the Radon-Nikodym theorem state?
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Evaluate \(f(x)=-a^3+6 a-7\) at \(a=-1\) and state the remainder.
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Simplify completely \(\mathrm{i}(7-\mathrm{i})\)
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What is a cubic equation? give an example and use latex.
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State the unique factorisation theorem and give an example
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What is the Pythagorean theorem and how do I use it?
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Was the Pythagorean School a cult?
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What was the significance of the invention of logarithms?
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What was the significance of the Pythagorean Theorem?
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In the diagram below, \(\mathrm{PR}\) is a chord of the circle with centre \(\mathrm{O}\). Diameter ST is perpendicular to PR at M. \(P R=8 \mathrm{~cm}, M T=2 \mathrm{~c...
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The roots of a quadratic equation are given as \(x=\dfrac{-2 \pm \sqrt{1-3 k}}{4}\).a) For which value(s) of \(k\) will the roots be real?b) For which value(s) of \(k\) w...
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How do you find the equation of a parabola given its vertex and focus?
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How do you find the slope of a line given two points?
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How do you factor a polynomial?
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What is the Navier-Stokes equations?
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What is a Green's theorem?
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What is a Stokes' theorem?
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What is the Pythagorean Theorem?
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What is the equation of the parabola with vertex at $(3,-2)$ and directrix $y=-1$?
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What is the slope of the line that passes through the points $(3,4)$ and $(6,8)$?
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What is the Pythagorean theorem?
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Prove that any polynomial of degree n has at most n roots.
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Show that \((x-1)\left(x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1\right)=x^9-1\) without multiplying the terms out.
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Calculate: \(\quad \sum_{n=1}^{\infty} 2.10^{1-n} \quad\) (if it exists)
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Factor the polynomial: \(x^2 + 4x + 4\)
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Find the vertex of the parabola: \(y = x^2 - 4x + 3\)
568
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Use the completing the square method to rewrite the quadratic equation \(y = x^2 - 2x + 1\) in vertex form.
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