# High school calculus questions and answers

Recent questions in Calculus and Analysis
Greyson Landry 2022-07-30

### Find the Taylor polynomial of degree n=4 for each function expanded about the given value of ${x}_{0}$.$f\left(x\right)={x}^{5}+4{x}^{2}+3x+1,{x}_{0}=0$

Zoagliaj 2022-07-30

### Stefan's Law of Radiation states that the radiation energy of abody is proportional to the fourth power of the absolute temperature T of a body. The rate of change of this energy ina surrounding medium of absolute temperature M is thus $\frac{dT}{dt}=k\left({M}^{4}-{T}^{4}\right)$where k > 0 is a constant. Show that the general solution of Stefan's equation is$\mathrm{ln}|\frac{M+T}{M-T}|+2{\mathrm{tan}}^{-1}\left(\frac{T}{M}\right)=4{M}^{3}kt+c$where c is an arbitrary constant.

Cristofer Graves 2022-07-30

### E and F are vector fields given by $E=2x{a}_{x}+{a}_{y}+yz{a}_{z}$ and $F=xy{a}_{x}-{y}^{2}{a}_{y}+xyz{a}_{z}$.Determine:(a)|E| at (1,2,3)

Deromediqm 2022-07-30

### Integral by use of substitution $\frac{3\mathrm{cos}xdx}{\sqrt{1+3\mathrm{sin}x}}$

Javion Henry 2022-07-30

### A regional Home Depot office issues approximately 1500 PO's per 40 hour work week to its suppliers. Through data collection, it is determined that the average value add time for a PO is 30 minutes. Assuming a Home Depot has world-class business processess, what is the lead time for any given PO to be issued? How many PO's would we expect to be in process at any given time?

przesypkai4 2022-07-30

### Find the length and direction of $u×v$ and $v×u$u = 2i - 2j + 4k, v = -i + j - 2k

vangstosiis 2022-07-29

### Find the sum of the series.$\sum _{n=1}^{\mathrm{\infty }}\frac{7}{{4}^{n}}$

stratsticks57jl 2022-07-29

### Solve. ${\int }_{0}^{\frac{\prod }{2}}﻿\prod 2{\mathrm{sin}}^{2}xdx$

Raegan Bray 2022-07-29

### Solve.$\mathrm{tan}1/2x=\mathrm{csc}x-\mathrm{cot}x$

beatricalwu 2022-07-28

### Find $L=\underset{n\to \mathrm{\infty }}{lim}\frac{4n+1}{2n+1}$. then determine ${ϵ}_{n}=L-{x}_{n}$ and find $\underset{n\to \mathrm{\infty }}{lim}{ϵ}_{n}$.

Parker Bird 2022-07-28

### $y=8{t}^{6}+{t}^{4}-\pi$what kind of functions is this, : polynomial, power, exponential,algebraic, trigometric, root, rational, and logarithmics?

Nelson Jennings 2022-07-28

### Find ${d}^{2}y/d{x}^{2}$ for the curve given by

Talon Mcbride 2022-07-28

### Find all the zeros ofthe function and write the polynomial as a product of linear factors:$f\left(x\right)=5{x}^{3}-9{x}^{2}+28x=6$

Livia Cardenas 2022-07-28

### Subtract the following matrices.$\left[\begin{array}{cc}-2& -9\\ 9& -7\\ 0& -1\end{array}\right]-\left[\begin{array}{cc}8& -7\\ 6& 6\\ -9& -7\end{array}\right]$

Violet Woodward 2022-07-28

### In A and B, cosine is given..find sine and tangent if x liesin the specific interval.A.) $\mathrm{cos}\left(x\right)=1/3x\in \left[\pi /2,0\right]$B.) $\mathrm{cos}\left(x\right)=-5/13x\in \left[\pi /2,\pi \right]$C.) $s=\mathrm{sec}\left(\pi x/2\right)$...Find the period. What symmetries does the function have?D.) $\mathrm{cos}\left(x+\pi /4\right)-1$. What is the period?

Awainaideannagi 2022-07-28

### Differentiate the function.$g\left(x\right)=3{x}^{-3}\left({x}^{4}-3{x}^{3}+15x-4\right)$

Graham Beasley 2022-07-28

### Find a polynomial function with integer coefficients that hasthe given zeros:1, 5i, -5i

Elsa Brewer 2022-07-28