Calculus Examples & Word Problems Solutions

High School
Calculus and Analysis

Recent questions in Calculus and Analysis

Cem Hayes 2020-10-23

Use the Integral Test to determine whether the infinite series is convergent.
$\sum_{n = 1}^{\infty} \frac{5}{4^{\ln n}}$

Ayaana Buck 2020-10-23

Find the limits
$lim_{x \to - 3} \frac{2 - \sqrt{x^{2} - 5}}{x + 3}$

floymdiT 2020-10-23

Use the Limit Comparison Test to determine the convergence or divergence of the series.
$\sum_{n = 1}^{\infty} \frac{1}{n^{2} (n^{2} + 4)}$

texelaare 2020-10-23

Identify a convergence test for the following series. If necessary, explain how to simplify or rewrite the series before applying the convergence test. You do not need to carry out the convergence test.
$\sum_{k = 3}^{\infty} \frac{2 k^{2}}{k^{2} - k - 2}$

Emeli Hagan 2020-10-23

Sketch a graph of the function. Use transformations of functions whenever possible. $f (x) = 3 x^{2}$

jernplate8 2020-10-23

Radius and interval of convergence Determine the radius and interval of convergence of the following power series.
$x - \frac{x^{3}}{4} + \frac{x^{5}}{9} - \frac{x^{7}}{16} + . . .$

lwfrgin 2020-10-23

The probability of rain in San Francisco on a given day is $\frac{1}{6}$ . The probability of rain in Miami is $\frac{5}{6}$ . Use two number cubes to find the simulated probability of rain in both cities.

vestirme4 2020-10-21

If $A = [\begin{matrix} 1 & 1 \\ 3 & 4 \end{matrix}], B = [\begin{matrix} 2 \\ 1 \end{matrix}], C = [\begin{matrix} - 7 & 1 \\ 0 & 4 \end{matrix}], D = [\begin{matrix} 3 & 2 & 1 \end{matrix}] and E = [\begin{matrix} 2 & 3 & 4 \\ 1 & 2 & - 1 \end{matrix}]$
Find , if possible,
a) A+B , C-A and D-E b)AB, BA , CA , AC , DA , DB , BD , EB , BE and AE c) 7C , -3D and KE

foass77W 2020-10-21

This is the quesetion. Suppose that a does not equal 0.
a. if $a \cdot b = a \cdot c$ , does it follow that $b = c$ ?
b. if $a \times b = a \times c$ , does it follow that $b = c$ ?
c. if $a \cdot b = a \cdot c$ and $a \times b = a \times c$ , does it follow that $b = c$ ?
Either prove the assertion is true in general or show that it is false for a concret choice of vectors a, b, c

Rivka Thorpe 2020-10-21

Find the Maclaurin series for the function. (Use the table of power series for elementary functions.)
$f (x) = \frac{e^{x^{4}}}{4}$

Bergen 2020-10-21

Representing functions by power series Identify the functions represented by the following power series.
$\sum_{k = 1}^{\infty} \frac{x^{2 k}}{k}$

FobelloE 2020-10-21

Given
$f (x) = x^{2}, g (x) = x + 7$
Find $(f \circ g) (x) .$
Find the domain of $(f \circ g) (x) .$
Find $(g \circ f) (x) .$
Find the domain of $(g \circ f) (x) .$
Find $(f \circ f) (x) .$
Find the domain of $(f \circ f) (x) .$
Find $(g \circ g) (x) .$
Find the domain of $(g \circ g) (x) .$

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?

foass77W 2020-10-20

Use the formula for the sum of a geometric series to find the sum.
$\sum_{n = 4}^{\infty} (- \frac{4}{9})^{n}$

ka1leE 2020-10-20

Show that the series converges. What is the value of the series?
$\sum_{n = 2}^{\infty} (- \frac{5}{3})^{n} (\frac{2}{5})^{n + 1}$

Kyran Hudson 2020-10-20

How are matrices added?

Bergen 2020-10-20

In this problem, allow $T_{1} : R^{2} \to R^{2}$ and $T_{2} : R^{2} \to R^{2}$ be linear transformations. Find $K e r (T_{1}), K e r (T_{2}), K e r (T_{3})$ of the respective matrices:
$A = [\begin{matrix} 1 & - 1 \\ - 2 & 0 \end{matrix}], B = [\begin{matrix} 1 & 5 \\ - 2 & 0 \end{matrix}]$

sagnuhh 2020-10-19

Let $M \in R^{10 \times 10}, s . t . M^{2020} = 0$ . Prove $M^{10} = 0$

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