Review calculus and integrating with inverse trig functions

 $f\left(x\right)=x^3$  What is the derivative of this function?

• 3x

•  $3x^2$  

•  $\frac{x^4}{4}+C$  

•  $3x^2+c$  

 $f\left(x\right)=5x^2$  What is the slope of the tangent line to the given function at the point x=1?

• 5/3

• 20

• 5

• 10

If f ' (x) > 0, what does that tell you about the graph of f(x)?

• The graph is concave up

• The graph is decreasing

• The graph is increasing

• The graph is concave up and the graph is increasing

What is the area between f(x) = 5/x and the x-axis over the region 2 to 3?

• 5/2

• 5 ln (3/2)

• 5 ln 3

• 5 ln 2

 $\int_{ }^{ }\ \frac{xdx}{\sqrt{9-x^2}}$  Which of the following methods would be most appropriate to solve the given integral?

• u-sub + power rule

• arcsine

• arctan

• U sub + natural log

 $\int_{ }^{ }\ \frac{dx}{\sqrt{9-x^2}}$  Which of the following options should be used to solve this integral?

• u-sub

• arctan

• arcsin

• cannot be solved with the methods learned so far.

 $\int_{ }^{ }\ \frac{dx}{\sqrt{x^2-9}}$  Which of the following options should be used to solve this integral?

• u-sub

• arctan

• arcsin

• cannot be solved with the methods learned so far.

 $\int_{ }^{ }\ \frac{dx}{x^2+9}$  Which of the following options should be used to solve this integral?

• u-sub

• arctan

• arcsin

• cannot be solved with the methods learned so far.

 $\int_{ }^{ }\ \frac{dx}{\sqrt{x^2+9}}$  Which of the following options should be used to solve this integral?

• u-sub

• arctan

• arcsin

• cannot be solved with the methods learned so far.

 $\int_{ }^{ }\ \frac{5xdx}{\sqrt{x^2+9}}$  Which of the following options should be used to solve this integral?

• u-sub

• arctan

• arcsin

• cannot be solved with the methods learned so far.