 # High school calculus questions and answers

Recent questions in Calculus and Analysis kuCAu 2020-10-20

### Flipping coins results in a probability of 0.4 heads for coin 1 and 0.7 heads for coin 2, respectively. One of these coins is picked at random and flipped a total of 10 times.(a) What is the probability that exactly 7 of the 10 flips land on heads? (b) Given that the first of these ten flips lands heads, what is the conditional probability that exactly 7 of the 10 flips lands on heads? Amari Flowers 2020-10-20

### A credit card contains 16 digits between 0 and 9. However, only 100 million numbers are valid. If a number is entered randomly, what is the probability that it is a valid number? Ava-May Nelson 2020-10-20

### What is the probability of obtain tails and an odd number? sagnuhh 2020-10-19

### Let $M\in {R}^{10×10},s.t.{M}^{2020}=0$. Prove ${M}^{10}=0$ Wierzycaz 2020-10-19

### Determine if the series converges or diverges. If the series converges find its sum $\sum _{n=1}^{\mathrm{\infty }}\frac{6}{\left(4n-1\right)\left(4n+3\right)}$ lwfrgin 2020-10-19

### Determine if the following series converge. If the series converges, calculate its value. Justify your answer. $\sum _{n=1}^{\mathrm{\infty }}\frac{{n}^{2}}{n!\left(\mathrm{log}\left(2\right){\right)}^{n}}$ Khadija Wells 2020-10-19

### a) Find the Maclaurin series for the function $f\left(x\right)=\frac{1}{1}+x$ b) Use differentiation of power series and the result of part a) to find the Maclaurin series for the function $g\left(x\right)=\frac{1}{\left(x+1{\right)}^{2}}$ c) Use differentiation of power series and the result of part b) to find the Maclaurin series for the function $h\left(x\right)=\frac{1}{\left(x+1{\right)}^{3}}$ d) Find the sum of the series $\sum _{n=3}^{\mathrm{\infty }}\frac{n\left(n-1\right)}{2n}$ This is a Taylor series problem, I understand parts a - c but I do not understand how to do part d where the answer is $\frac{7}{2}$ hexacordoK 2020-10-19

### Determine the limits if they exist: $\underset{\left(x,y\right)\to \left(2,4\right)}{lim}\frac{\left(x-2{\right)}^{2}\left(y-4{\right)}^{2}}{\left(x-2{\right)}^{3}+\left(y-4{\right)}^{3}}$ illusiia 2020-10-18

### Find the limits $\underset{x\to 9}{lim}\frac{\mathrm{sin}\left(\sqrt{x}-3\right)}{x-9}$ Anish Buchanan 2020-10-18

### Graph each polynomial function. melodykap 2020-10-18

### Find the composite functions $f\circ g$ and $g\circ f$. Find the domain of each composite function. Are the two composite functions equal? $f\left(x\right)={x}^{2}-1$ g(x) = −x generals336 2020-10-18

### Evaluate the following limits. $\underset{\left(x,y\right)\to \left(6,2\right)}{lim}\frac{{x}^{2}-3xy}{x-3y}$ Jerold 2020-10-18

### Evaluate the integrals. $\int {e}^{ln\sqrt{x}}dx$ Anonym 2020-10-18

### Determine the exact value of expression. $\mathrm{sec}\left(210\right)×\mathrm{cot}\left(300\right)+\mathrm{sin}\left(225\right)$ Cabiolab 2020-10-18

### Confirm that the Integral Test can be applied to the series. Then use the Integral Test to determine the convergence or divergence of the series. $\sum _{n=1}^{\mathrm{\infty }}\frac{1}{{\left(2n+3\right)}^{3}}$ Lennie Carroll 2020-10-18 vazelinahS 2020-10-18