Question 1: Solve the following logarithmic equation. ln(5x) ln(x + 1) = 1

Question 2 Find a and b so that f(x) is continuous everywhere. f(x) = ax + b x 0

x 2 2 ; 0 < x 1

bx + a ; x > 1

Question 3 Find the slope of the tangent line to the graph y = 6 8x + 1 when x = 1.

Question 5 (10 points) Using only the definition of derivative as a limit, calculate f ' (x) where f(x) = 3 /2 x .

Find the equation of the tangent line to the curve f(x) = x ln(x 4) at x = 5.