Question 1: For each of the following, find (if applicable) and show your work:

Question 1: For each of the following, find (if applicable) and show your work:

-x and y-intercept

-Sign chart

-Horizontal, vertical, and slant asymptotes

-End behavior

-Critical points (Max and Min)

-Slope chart

-Points of inflection

-Concavity chart

-And sketch each function

a) y=(x^2-4)/x^2

b) y=1/(x^2-1)

c) y=(x^2)/(e^x)

d) y=sin(x^2) for -2pi<=x<=2pi

Question 2: Find the derivative of the following function, y=2^(5x+7)(ln(5x+1)).

Question 3: Use the process of implicit differentiation to find dy/dx given that x^3e^y-ye^x=0.

Question 4: Use logarithmic differentiation to find the derivative of the function y=((2x+5)^3(5x^2-2x)^4)/sqrt((2x+5)).

Question 5: From the first principles (ie using the tangent slope method), find the slope of the following curves at the given value of x.

a) f(x)=2x^2-6x at x=3

b) y=3x^3+1 at x=-4

Question 6: Determine the following limit (if it exists). lim x->4 ((x^2+x-20)/(8-2x))

Question 7: Evaluate the following limit (if it exists). lim x->0 ((sqrt(x+16)-4)/x)