BC Calculus "Final" version 2

Find the derivative for  $f\left(x\right)=e^{\sin x}$  

•  $e^{\cos x}$  

•  $\cos x\ \left(e^{\sin x}\right)$  

•  $\frac{1}{\cos\ x}e^{\sin x}$  

•  $-e^{\cos x}$  

what is the average rate of change of the function
 $f\left(x\right)=x^2+x$  on the interval  $\left(0,\ 4\right)$  ?

• 5

• 1

• 20

• 1/5

Let  $g\left(x\right)=\int_0^{2x}f\left(t\right)\ dt.$  where  $f\left(t\right)$  is the function whose graph is shown in the figure. Estimate  $g\left(4\right)$  

• 4

• -8

• 12

• 20

Find  $F'\left(x\right)$ .  $F\left(x\right)=\int_0^{2x}\sin\left(t^2\right)dt$  

•  $2\sin\left(4x^2\right)$  

•  $2\cdot\sin\left(2x\right)$  

•  $\frac{\cos\left(2x^2\right)}{2}$  

•  $x^{2\ }\cdot\sin\left(x^{12}\right)$  

List all of the x-locations of the minimum points of the function whose derivative is graphed.

• {-2, 1}
• {-1, 1}
• {-1}
• Cannot be determined}

What curve do the parametric equations make? What is the direction of motion?

x=1+3sint

y=-2+4cost

• Circle. Counterclockwise.

• Circle. Clockwise.

• Ellipse. Counterclockwise.

• Ellipse. Clockwise.

 $\sin y=5x^4-5$ Find the slope of this curve at the point  $\left(1,\pi\right)$  (hint: use implicit differentiation)

•  $-\frac{1}{20}$  

•  $20$  

•  $-20$  

• undefined

 $if\ f\left(0\right)=0,\ f'\left(0\right)=1,\ f''\left(0\right)=0,\ \&\ f'''\left(0\right)=2,$  Find the 3rd order Taylor Polynomial generated by f(x) at x=0

•  $\frac{1}{3}x^3+x$  

•  $\frac{1}{3}x^3+\frac{1}{2}x$  

•  $\frac{2}{3}x^3+x$  

•  $2x^3+x$  

 $1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...$ 

To what number does this series Converge?

• 1/2

• 2

• 3/2

• It is Divergent

 $v\left(t\right)=t^2-6t+8,\ \ \ 0\le t\le5$  

What is the displacement of a particle with the given velocity equation over the given interval? Give answer correct to three decimal places.

• 6.667

• 9.333

• 12.333

• 13.333