Topic
Q:
\( \int _ { 0 } ^ { \frac { 1 } { 2 } } e ^ { x ^ { 2 } } = \)
Q:
Evaluate the integral
\( \int(2 x+5)\left(x^{2}+5 x+5\right)^{5} d x \)
by making the substitution \( u=x^{2}+5 x+5 \)
\( +C \)
Q:
Evaluate the integral
\( \int(2 x+5)\left(x^{2}+5 x+5\right)^{5} d x \)
by making the substitution \( u=x^{2}+5 x+5 \)
\( +C \)
Q:
Given the following two functions:
\[ f(x)=\frac{2 x}{x+1} \]
\[ g(x)=\frac{3 x-1}{x^{2}} \]
Find the limit of the product \( h(x)=f(x) \cdot g(x) \) as \( x \) approaches infinity.
Q:
A 25 -year old woman burns \( 350-70 t \mathrm{cal} / \mathrm{hr} \) while walking on her treadmill. Her caloric intake from
drinking Gatorade is \( 135 t \) calories during the \( t \) th hour. What is her net decrease in calories after walking
for 4 hours?
\( \square \)
Q:
Suppose that a particle moves along a straight line with velocity \( v(t)=12-1 t \), where \( 0 \leq t \leq 2 \) (in
meters per second). Find the formula for the displacement of the particle and the total distance it has
traveled at time \( t=2 \) seconds.
Displacement at time \( t \) is:
Q:
Suppose that a particle moves along a straight line with velocity \( v(t)=12-1 t \), where \( 0 \leq t \leq 2 \) (in
meters per second). Find the formula for the displacement of the particle and the total distance it has
traveled at time \( t=2 \) seconds.
Displacement at time \( t \) is:
Total distance traveled:
Q:
Suppose that in a memory experiment the rate of memorizing is given by \( M^{\prime}(t)=-0.005 t^{2}+0.6 t \),
where \( M^{\prime}(t) \) is the memory rate, in words per minute. How many words are memorized in the first 10
minutes?
words
Q:
The traffic flow rate (cars per hour) across an intersection is \( r(t)=300+900 t-90 t^{2} \), where \( t \) is in
hours, and \( t=0 \) is 6 am . How many cars pass through the intersection between 6 am and 11 am?
cars
Q:
\( \int e ^ { x ^ { 2 } } = \)
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