Calculus Examples & Word Problems Solutions

High School
Calculus and Analysis

Recent questions in Calculus and Analysis

hexacordoK 2020-10-19

Determine the limits if they exist: $lim_{(x, y) \to (2, 4)} \frac{(x - 2)^{2} (y - 4)^{2}}{(x - 2)^{3} + (y - 4)^{3}}$

Khadija Wells 2020-10-19

a) Find the Maclaurin series for the function
$f (x) = \frac{1}{1} + x$
b) Use differentiation of power series and the result of part a) to find the Maclaurin series for the function
$g (x) = \frac{1}{(x + 1)^{2}}$
c) Use differentiation of power series and the result of part b) to find the Maclaurin series for the function
$h (x) = \frac{1}{(x + 1)^{3}}$
d) Find the sum of the series
$\sum_{n = 3}^{\infty} \frac{n (n - 1)}{2 n}$
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 $\frac{7}{2}$

lwfrgin 2020-10-19

Determine if the following series converge. If the series converges, calculate its value. Justify your answer.
$\sum_{n = 1}^{\infty} \frac{n^{2}}{n! (\log (2))^{n}}$

Wierzycaz 2020-10-19

Determine if the series converges or diverges. If the series converges find its sum
$\sum_{n = 1}^{\infty} \frac{6}{(4 n - 1) (4 n + 3)}$

vazelinahS 2020-10-18

Find x,y,z and w
$[\begin{matrix} x & 5 & (2 x - 1) \\ y & 4 & 4 y \end{matrix}] = [\begin{matrix} (2 x - 3) & z & 5 \\ 7 & (2 + 1) & (3 y + 7) \end{matrix}]$

Lennie Carroll 2020-10-18

Define Hermitian Matrices.

Jerold 2020-10-18

Evaluate the integrals.
$\int e^{l n \sqrt{x}} d x$

generals336 2020-10-18

Evaluate the following limits.
$lim_{(x, y) \to (6, 2)} \frac{x^{2} - 3 x y}{x - 3 y}$

illusiia 2020-10-18

Find the limits
$lim_{x \to 9} \frac{\sin (\sqrt{x} - 3)}{x - 9}$

Anish Buchanan 2020-10-18

Graph each polynomial function. $f (x) = x^{4} - x^{3} - 6 x^{2} + 4 x + 8$

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?
$f (x) = x^{2} - 1$
g(x) = −x

Anonym 2020-10-18

Determine the exact value of expression.
$\sec (210) \times \cot (300) + \sin (225)$

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.
$\sum_{n = 1}^{\infty} \frac{1}{{(2 n + 3)}^{3}}$

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