AP Calculus BC Review Activity

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

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

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

 f(x) =  $\frac{x-3}{x^2+3x}$  

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?

Find the derivative of 

y = $\frac{1}{2}e^x-3\sin x$  

find the value of f'( $\pi$ ) if 

f(x) =  $\frac{\sec x}{x}$  

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

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

find the value of f''(x) if

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