AP Calculus BC Review Activity

 $\lim_{x\rightarrow-3}\ \frac{x^2-9\text{x}}{2x^2+7x+3}$  

• 5/6

• 6/5

• -3

• DNE

 $\lim_{x\rightarrow\infty}\ \frac{5x^3-3}{x^2}$  

•  $\infty$  

•  $-\infty$  

• 0

• 5

At what x-value(s), if any, does f(x) have vertical asymptotes?

 f(x) =  $\frac{x-3}{x^2+3x}$  

• x = 0

• x = -3

• x = 0  &  x = 3

• No VA

Is the function F(x) = $\frac{x^2+4x-32}{x^2-2x-8}$  
continuous? If not, at what x-value(s) is the discontinuity located?

• Yes, continuous

• No, at x = -2

• No, at x = 4

• No, at x = -2  &  x = 4

Find the derivative of 

y = $\frac{1}{2}e^x-3\sin x$  

• y' =  $\frac{1}{2}e-3\cos x$  

• y' =  $\frac{1}{2}xe-3\sin x$  

• y' =  $\frac{1}{2}e^x-3\sin x$  

• y' =  $\frac{1}{2}e^x-3\cos x$  

find the value of f'( $\pi$ ) if 

f(x) =  $\frac{\sec x}{x}$  

•  $-\pi^2$  

•  $\frac{1}{\pi^2}$  

•  $-\frac{1}{\pi}$  

• 0

Find the equation of the line tangent to g(x) = $16x^{-2}-4x^{\frac{1}{2}}$  at  x = 4

• y - 7 = 3/2(x-4)

• y - 4 = -2/3(x+7)

• y = -3/2(x - 4)

• y + 7 = -3/2(x-4)

Given the point (0,2) occurs on the function f(x) = $e^x+\cos\left(x\right)$ , find the equation of the tangent line at that point. 

• y + 2 = x

• y = x + 2

• y = 2x

• y = 1/2x

Find the derivative of $f\left(x\right)\ =\ \tan\left(5x\right)^2$  

•  $f'\left(x\right)=10\tan\left(5x\right)$  

•  $f'\left(x\right)=10\sec^2\left(5x\right)\tan\left(5x\right)$  

•  $f'\left(x\right)=2\sec^2\left(x\right)\tan\left(x\right)$  

•  $f'\left(x\right)=10\sec^2\left(5x\right)$  

find the value of f''(x) if

 $f\left(x\right)=\left(\ln x\right)^2$  

•  $\frac{1}{e}$  

•  $\frac{1}{\sqrt{e}}$  

•  $-\frac{2}{e}$  

•  $e^{-2}$