# Calculus

20) 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

ans is B. Explain

21) d/dx(sin(cosx)) = ? Explain

22) 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

23) Integral of cos^2xsinxdx =? Explain

24) d/dx Integral with x on top and 1 on bottom of t^2dt=? Explain

25) Let r(t) be a differentiable function 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) = ?

Ans =2? Explain.

https://brainmass.com/math/calculus-and-analysis/calculus-15025

#### Solution Preview

20.)

Because, function is continuous at all the points.

Hence,

Lt(h->0) f(a+h)-f(a)/h = differentiation of f(x) at x = a which is acceptable, only when f(x) is continuous at x = a

Therefore, correct answer is B.

21.)

d/dx (sin(cosx)) = ...

#### Solution Summary

There are a variety of calculus topics shown here, including differentiability, continuity, integration, and rate of change