# High school calculus questions and answers

Recent questions in Calculus and Analysis
Tazmin Horton 2020-11-07

### If A and B are 3×3 invertible matrices, such that det(A)=2, det(B) =-2. Then det$\left(AB{A}^{T}\right)=???$

Caelan 2020-11-07

### If A and B are $4×4$ matrices, det(A) = 1, det(B) = 4, then det(AB) = ? det(3A) = ? $det\left({A}^{T}\right)=?$ $det\left({B}^{-1}\right)=?$ $det\left({B}^{4}\right)=?$

waigaK 2020-11-07

### write B as a linear combination of the other matrices, if possible. $B=\left[\begin{array}{cc}2& 3\\ -4& 2\end{array}\right],{A}_{1}=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right],{A}_{2}=\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right],{A}_{3}=\left[\begin{array}{cc}1& 1\\ 0& 1\end{array}\right]$

Tazmin Horton 2020-11-07

### Find the limits $\underset{x\to 0}{lim}\frac{\frac{1}{x-1}+\frac{1}{x+1}}{x}$

vestirme4 2020-11-06

### Determine the convergence or divergence of the series. $\sum _{n=2}^{\mathrm{\infty }}\frac{1}{n\left(\mathrm{ln}n{\right)}^{3}}$

Yasmin 2020-11-06

### Evaluate these integrals. $\int \sqrt{{e}^{x}+1}dx$

jernplate8 2020-11-06

### Use transformations to sketch the graph of the function.

permaneceerc 2020-11-05

### Prove: If A and B are $n×n$ diagonal matrices, then AB = BA.

nagasenaz 2020-11-05

### 1)What is the position vector r(t) as a function of angle $\theta \left(t\right)$. For later remember that $\theta \left(t\right)$ is itself a function of time.Give your answer in terms of $R,\theta \left(t\right)$, and unit vectors x and y corresponding to the coordinate system in thefigure. 2)For uniform circular motion, find $\theta \left(t\right)$ at an arbitrary time t.Give your answer in terms of $\omega$ and t.3)Find r, a position vector at time.Give your answer in terms of R and unit vectors x and/or y.4)Determine an expression for the positionvector of a particle that starts on the positive y axis at (i.e., at ,$\left({x}_{0},{y}_{0}\right)=\left(0,R\right)$) and subsequently moves with constant $\omega$.Express your answer in terms of R, $\omega$ ,t ,and unit vectors x and

Clifland 2020-11-05

### Use ana appropriate test to determine whether the series converges. $\sum _{k=1}^{\mathrm{\infty }}\left(\frac{k!}{{20}^{k}{k}^{k}}\right)$

hexacordoK 2020-11-05

### Solve by using De Moivre's Theorem (find real and imaginary part of complex number):${\left(\sqrt{3}+i\right)}^{3}$

tinfoQ 2020-11-05

### Using calculus, it can be shown that the arctangent function can be approximated by the polynomial where x is in radians. a) Use a graphing utility to graph the arctangent function and its polynomial approximation in the same viewing window. How do the graphs compare? b) Study the pattern in the polynomial approximation of the arctangent function and predict the next term. Then repeat part (a). How does the accuracy of the approximation change when an additional term is added?

Tobias Ali 2020-11-03

### Find x such that the matrix is ​​equal to its inverse.$A=\left[\begin{array}{cc}7& x\\ -8& -7\end{array}\right]$

Kyran Hudson 2020-11-02

### Use the alternating series test to determine the convergence of the series $\sum _{n=1}^{\mathrm{\infty }}\left(-1{\right)}^{n}{\mathrm{sin}}^{2}n$

zi2lalZ 2020-11-02

### Find the area of the region below $y={x}^{2}–3x+4$ and above $y=6f\phantom{\rule{1em}{0ex}}\text{or}\phantom{\rule{1em}{0ex}}3\le x\le 6$

FobelloE 2020-11-02

### Find the tangential and normal components of the acceleration vector $r\left(t\right)=\left(3t-{t}^{3}\right)i+3{t}^{2}j$

Reeves 2020-11-02

### Show that B is the inverse of A. $A=\left[\begin{array}{cc}1& -1\\ -1& 2\end{array}\right],B=\left[\begin{array}{cc}2& 1\\ 1& 1\end{array}\right]$

illusiia 2020-11-01