# Recent questions tagged theorem

35
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Describe the Residue Theorem and its applications.
36
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State and explain Cauchy's Integral Theorem.
32
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What is the Intermediate Value Theorem (IVT)?
43
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What is the Bolzano-Weierstrass theorem?
66
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Prove Bezout's Theorem for Plane Curves
66
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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.
76
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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...
91
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Find (a) all horizontal and (b) all vertical asymptotes of the graph$y=\frac{|x| \sqrt{4 x^{4}+6 x^{2}+4}}{(2 x-1)^{2}(x+1)}$
122
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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?
96
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What is Fermat's Little Theorem?
112
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What is the main result of the Chinese Remainder Theorem?
81
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What is the fundamental theorem of arithmetic?
100
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State the equipartition theorem
122
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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...
113
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Find the vertical and horizontal asymptotes of the graph of the function $$f(x)=\sqrt{x+1}-\sqrt{x}$$.
158
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Find the vertical and horizontal asymptotes of the graph of the function $$f(x)=(2 x+3) / \sqrt{x^{2}-2 x-3}$$.
128
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Find any vertical and horizontal asymptotes of the graph of the function $$f(x)=(4 x-5) /(3 x+2)$$.
73
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State Green's theorem in the plane.
58
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State Gauss' Theorem
169
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Is the angle between the tangent and the chord equal to the angle in the alternate segment?
163
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What is the Fermat's Last Theorem?
168
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What is the Pythagoras's Theorem for?
109
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Regarding polynomials – What does the remainder theorem consist of?
290
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What does the Radon-Nikodym theorem state?
220
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Evaluate $$f(x)=-a^3+6 a-7$$ at $$a=-1$$ and state the remainder.
522
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Simplify completely $$\mathrm{i}(7-\mathrm{i})$$
744
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What is a cubic equation? give an example and use latex.
576
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State the unique factorisation theorem and give an example
570
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What is the Pythagorean theorem and how do I use it?
337
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Was the Pythagorean School a cult?
325
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What was the significance of the invention of logarithms?
504
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What was the significance of the Pythagorean Theorem?
603
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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... 381 views 1 answers 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$$ w...
278
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How do you find the equation of a parabola given its vertex and focus?
301
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How do you find the slope of a line given two points?
517
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How do you factor a polynomial?
483
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What is the Navier-Stokes equations?
336
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What is a Green's theorem?
607
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What is a Stokes' theorem?
604
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What is the Pythagorean Theorem?
471
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What is the equation of the parabola with vertex at $(3,-2)$ and directrix $y=-1$?
405
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What is the slope of the line that passes through the points $(3,4)$ and $(6,8)$?
377
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What is the Pythagorean theorem?
366
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Prove that any polynomial of degree n has at most n roots.
313
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Show that $$(x-1)\left(x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1\right)=x^9-1$$ without multiplying the terms out.
342
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Calculate: $$\quad \sum_{n=1}^{\infty} 2.10^{1-n} \quad$$ (if it exists)
Factor the polynomial: $$x^2 + 4x + 4$$
Find the vertex of the parabola: $$y = x^2 - 4x + 3$$
Use the completing the square method to rewrite the quadratic equation $$y = x^2 - 2x + 1$$ in vertex form.