Solve the following:
Q1. Differentiate
a. Y = 3x + PI^3
b. Y = 1 / (x-3)^3
c. y = (x^4 - x)^3 (3x + 2)^4
d. Y = (1 + x - x^3)^4
Q2. Compute the following limits.
a. limx→∞[(x-2)/(x^2+2)]
b. limx→∞[(3x^5- 6x^4+ 2x-6)/(7x^5- 2x^2+ 10,000)]
Q3. Use limits to compute f"(3) where f (x) = x^2 - 2x +3.
Q4. a. What is the average rate of change of f(x) given f(x) = -6/x from [1,2] and [1,4].
b. What is the instantaneous rate of change of f(x) when x = 1.
Q5. Write the equation of the tangent line to the curve y = x^3 - 2x^2 +5 at x = 2.