How do I solve the problem: [math] A=\begin{pmatrix} -2 &4 \\   -5& 7 \end{pmatrix}, A^{n}=? [/math]?
Given [math]A[/math], What is the general formula of [math]A^n[/math]? If [math]A=\begin{pmatrix} -2 &4 \\ -5& 7 \end{pmatrix}[/math], what is the [math]A^n[/math]?
How does one calculate [math]\int \frac1{x^2+a^2}dx[/math]? What is [math]x^2+\frac{1}{x^2}[/math], given [math]x+\frac{1}{x}= 1[/math]? How do you determine an expression in terms of [math]A^{-1}[/math] and [math]B^{-1}[/math] for [math]((AB)^T)^{-1}[/math] with [math]A[/math] and [math]B[/math] being matrices of [math]m\times n[/math] size? If a function [math]f(x)[/math] is defined as [math]f(x) = x ^ 3 + 3x + 1[/math], then what is [math]f ^ {-1}(x)[/math]? Find [math]S=\sum _{k=1}^n\left(-1\right)^k\begin{pmatrix}2n-k\\ k\end{pmatrix}[/math]? How does one calculate [math]\frac{1}{1 \times 2} [/math] + [math]\frac{1}{3 \times 4}[/math] + … ? What is [math]\dfrac{d}{dx}\left(\sin^{-1}(x)+2\sqrt{1-x^2}\right)[/math]? Where [math]x\in(-1,1)[/math]. If [math]\sqrt{a}+\sqrt{a}=20[/math], then what is the value of [math]a[/math]? What is [math]f(x)[/math] if [math]ff(x)[/math] or [math]f^2(x) =(x[/math][math]^4+[/math][math]4x^3+3x^2+4x+2[/math][math])^4?[/math] What is [math]\displaystyle\int x\sqrt{x^2+x+1}\,dx[/math] ? If [math]f(f(x)) =x^2-x+1[/math], what is [math]f(0)[/math]? What is [math]f(x)[/math] in the math problem [math]f(x)=x+f(1+\frac{1}{x})?[/math] What is [math]x[/math] if [math]x^8=1[/math]? How do I show that [math]|\alpha| \leq max[/math] {[math]1, \sum_{i=0}^{n-1} |a_i|[/math]} where [math]\alpha [/math] is zero of [math]p(x)=\sum_{i=0}^{n} a_i x^i,[/math] where [math]a_i[/math] may be complex and [math]a_n =1[/math]? What is the value of [math]2x^2 - 7x^2 -2x + 1[/math] if [math]x=\frac{1}{2 + \sqrt{3}}[/math]? What is the value of [math]\sum_{n = 1}^{\infty}(-1)^{n-1}\frac{3}{n^4}[/math]? How would you calculate [math]\sum_{n=1}^\infty \frac{1}{2^n} \cdot \frac{1}{n - \frac45}[/math]? If f(x) = 7 x +12, what is [math]f^{-1}[/math](x) (the inverse function)? What is [math]\displaystyle \lim_{n \to \infty}\scriptstyle \sqrt{1 +2 \sqrt{1 +3 \sqrt{1 +4 \sqrt{\ldots \sqrt{1+n}}}}}[/math]? What is [math]\sqrt {2+\sqrt {2+\sqrt {2+\sqrt {2+...\infty}}}}[/math] ? What is the value of [math]\sum_ {n=1} ^ {\infty} n^ {-n}[/math]? How do you evaluate [math]\int_0^1\frac{x-1}{\ln x}\, dx[/math]? If [math]X[/math] and [math]Y[/math] are two independent discrete random variables such that [math]X\sim\text{Bin}(n,p)[/math] and [math]Y\sim\text{Bin}(m,p)[/math]. How do I interpret [math]Z=X+Y\sim\text{Bin}(m+n,p)[/math] as the sum of two functions [math]X[/math] and [math]Y[/math] ? How can I evaluate [math]\int \frac{x^4+1}{x^6+1}\mathrm{d}x[/math]? What is [math]\displaystyle \lim_{n \to \infty}\scriptstyle \sqrt{1+ \sqrt{2 +\sqrt{3 + \sqrt{\ldots \sqrt{n}}}}}[/math]? What is the value of [math]x[/math] in this equation: [math]3=\frac {6\sqrt {12,3}}{\sqrt {x}}[/math]? If [math]6 \sin 3x - \cos^2 2y = 6[/math] Then what is the value of [math]x[/math]? What is [math]\frac{d}{dx} \left(\sin(2x)\cos(2y)=0\right)[/math]? What is [math]\frac{d}{dx}(2x)^2[/math]? How can one evaluate [math]\displaystyle\int \frac{\sqrt{x-2}}{x+1} \, dx[/math]?