Calculus Examples & Word Problems Solutions

High School
Calculus and Analysis

Recent questions in Calculus and Analysis

Sinead Mcgee 2020-10-31

Factor the polynomial. $r^{4} - 81$

emancipezN 2020-10-31

How is called the set of all images of the elements in the domain of a function?

midtlinjeg 2020-10-28

Consider the three following matrices:
$A = [\begin{matrix} 1 & 0 & 0 \\ 0 & - 1 & 0 \\ 0 & 0 & 1 \end{matrix}], B = [\begin{matrix} 1 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & - 1 \end{matrix}] and C = [\begin{matrix} 0 & - i & 0 \\ i & 0 & - i \\ 0 & i & 0 \end{matrix}]$
Calculate the Tr(ABC)
(a)1
(b)2
(c)2i
(d)0

Albarellak 2020-10-28

Find a polynomial with integer coefficients that satisfies the given conditions. Q has degree 3 and zeros 0 and i.

Brennan Flores 2020-10-28

Solve it please $7^{2} = ?$

Annette Arroyo 2020-10-28

Let $a_{n} \to 0$ , and use the Algebraic Limit Theorem to compute each of the following limits (assuming the fractions are always defined):
$lim_{n \to \infty} \frac{1 + 2 a_{n}}{1 + 3 a_{n} - 4 (a_{n})^{2}}$

a2linetagadaW 2020-10-28

Evaluate the following integrals.
$\int \sec^{4} x d x$

glasskerfu 2020-10-28

Find the gradient vector field $\vec{F} = \nabla f$ for each of the function $f (x, y, z) = \sqrt{x^{2} + y^{2} + z^{2}}$

ossidianaZ 2020-10-28

Find the limits
$lim_{(x, y) \to (3, 4)} \sqrt{x^{2} + y^{2} - 1}$

CoormaBak9 2020-10-28

Functions to power series Find power series representations centered at 0 for the following functions using known power series. Give the interval of convergence for the resulting series.
$f (x) = \ln \sqrt{4 - x}$

Tazmin Horton 2020-10-28

Find the limit
$lim_{x \to 0} \frac{x \sin x}{2 - 2 \cos x}$

babeeb0oL 2020-10-28

Which of the series, and which diverge?
Give reasons for your answers. (When you check an answer, remember that there may be more than one way to determine the series’ convergence or divergence.)
$\sum_{n = 1}^{\infty} \frac{1}{2 n - 1}$

Trent Carpenter 2020-10-27

Find the limit:
$lim_{n \to \infty} (\frac{1}{n + 1} + \frac{1}{n + 2} + . . . + \frac{1}{2 n})$

Maiclubk 2020-10-27

Which of the series, and which diverge?
Give reasons for your answers. (When you check an answer, remember that there may be more than one way to determine the series’ convergence or divergence.)
$\sum_{n = 1}^{\infty} \frac{3}{\sqrt{n}}$

Wierzycaz 2020-10-27

If possible, find scalars $c_{1}, c_{2}, and c_{3}$ so that
$c_{1} [\begin{matrix} 1 \\ 2 \\ - 3 \end{matrix}] + c_{2} [\begin{matrix} - 1 \\ 1 \\ 1 \end{matrix}] + c_{3} [\begin{matrix} - 1 \\ 4 \\ - 1 \end{matrix}] = [\begin{matrix} 2 \\ - 2 \\ 3 \end{matrix}]$

CoormaBak9 2020-10-27

Use L'Hospital Rule to find the limits $\lim_{x \to 0} \frac{s i n m x}{s i n n x}$

Cabiolab 2020-10-27

Let $A = [\begin{matrix} 2 & - 1 & 5 \\ - 3 & 4 & 0 \end{matrix}] and B = [\begin{matrix} - 3 & - 4 & 2 \\ - 1 & 0 & - 5 \end{matrix}]$
Find each result.
3A+2B=?
A-3B=?

sagnuhh 2020-10-27

Formulate the method for adding partitioned matrices,
and verify your method by partitioning the matrices in two different ways and finding their sum.
$A = [\begin{matrix} 1 & 3 & - 1 \\ 2 & 1 & 0 \\ 2 & - 3 & 1 \end{matrix}] and B = [\begin{matrix} 3 & 2 & 1 \\ - 2 & 3 & 1 \\ 4 & 1 & 5 \end{matrix}]$

Nannie Mack 2020-10-27

Find two different $2 \times 2$ matrices A such that $A^{2} = O$ .

tinfoQ 2020-10-27

For each of the pairs of matrices that follow, determine whether it is possible to multiply the first matrix times the second. If it is possible, perform the multiplication.
$[\begin{matrix} 1 & 4 & 3 \\ 0 & 1 & 4 \\ 0 & 0 & 2 \end{matrix}] [\begin{matrix} 3 & 2 \\ 1 & 1 \\ 4 & 5 \end{matrix}]$

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Calculus and Analysis

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