Topic
Q:
Evaluate the integral of the product of two functions:
\[ \int\left(2 x^{2} \cdot e^{x}\right) d x \]
Q:
Consider the indefinite integral \( \int x \cdot \sqrt[2]{x^{2}+6} d x \) :
This can be transformed into a basic integral by letting
\( u=\square \) and
\( d u=\square \)
Q:
A television production company charges a basic fee of \( \$ 7,000 \) and then \( \$ 4,000 \) an hour when filming a commercial.
(a) Write a linear equation that describes the relationship between the total production costs \( c \) and the hours \( h \) of filming.
(b) Use your answer to part (a) to find the production costs if a commercial required 9 hours of filming.
Q:
Complete the square of the given quadratic
expression. Then, graph the function using the technique
of shifting.
\( f(x)=x^{2}-6 x \)
Complete the square by entering the correct numbers into
the expression below.
\( f(x)=(x+\square)^{2}+\square \)
Q:
Evaluate the integral of the product of two functions:
\[ \int\left(2 x^{2} \cdot e^{x}\right) d x \]
Q:
The diameter of a circle measures 20 ft. What is the circumference of the circle?Use 3.14 for π, and do not round your answer. Be sure to include the correct unit in your answer.
Q:
Evaluate the integral
by making the appropriate substitution: \( u=\square \frac{d x}{(2 x+2)^{4}} \),
\( \int \frac{d x}{(2 x+2)^{4}}=\square \)
Q:
Evaluate the indefinite integral.
\( \int \frac{5}{(t+3)^{2}} d t \)
\( \square+C \)
Q:
Given two sequences \( \left\{a_{n}\right\} \) and \( \left\{b_{n}\right\} \) :
\[ \begin{aligned} a_{n} & =\frac{2 n}{n+1} \\ b_{n} & =\frac{1}{n^{2}}\end{aligned} \]
Q:
Add the polynomials: (x^4 + 3x^3 - x) + (2x^4 - 5x^3 + 4).
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