Assignment:
Q1. If the function f is continuous for all real numbers and lim as h approaches 0 of f(a+h) - f(a)/ h = 7 then which statement is true?
a) f(a) = 7
b) f is differentiable at x=a.
c) f is differentiable for all real numbers.
d) f is increasing for x>0.
e) f is increasing for all real differentiable
Q2. d/dx(sin(cosx)) = ? Explain
Q3. Which of the following is true for y=x^4-2x^3? Ans is the curve has two points of inflection and one relative extremum. Explain
Q4. Integral ofcos^2xsinxdx =? Explain
Q5. d/dxIntegral with x on top and 1 on bottom of t^2dt=? Explain
Q6. Let r(t) be a differentiable functon that is positive and increasing. The rate of increase of r^3 is equal to 12 times the rate of increase of r when r(t) = ?
Provide complete and step by step solution for the question and show calculations and use formulas.