CONTINUITY AND DIFFERENTIABILITY - L0

Continuity & Differentiability - Continuity|Condition For Continuity|Doubtful Points|Questions|OMR

The function f(x)=e^(|x|) is (a) Continuous everywhere but not differentiable at x=0 (b) Continuous and differentiable everywhere (c) Not continuous at x=0 (d) None of the above

Continuity & Differentiability -Condition For Continuity|Questions|Types Of Discontinuity|Questions|Differentiability|OMR

Let f : R rarr R satisfying l f (x) l <= x^2 for x in R, then (A) f' is continuous but non-differentiable at x = 0 (B) f' is discontinuous at x = 0 (C) f' is differentiable at x = 0 (D) None of these

Continuity And Differentiability |Excercise Questions

Let f(x)=[x e^x\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ xlt=0x+x^2-x^3\ \ \ \ \ \ x >0 then prove that f is continuous and differentiable for all xdot f' is continuous and differentiable for all xdot

The function f(x)=[(sqrt(x))/(1+x)] ; (where [ ] denotes the greatest integer function) is (A) Continuous but non-differentiable for x>0 (B) Continuous and differentiable for x>=0 (C) Discontinuous exactly at two points for x>=0 (D) Non-differentiable exactly at one point for x>0

Which of the following is not true? (A) A polynomial function is always continuous (B) A continuous function is always differentiable (C) A differentiable function is always continuous (D) None of these

Assertion (A) : A continuous function is always differentiable. Reason (R ) : A differentiable function is always continuous.

If f(x)={s in(cos^(-1)x)+cos(sin^(-1)x),xlt=0s in(cos^(-1)x)-cos(sin^(-1)x ,x >0) . Then at x=0 f(x) is continuous and differentiable f(x) is continuous but not differentiable f(x) not continuous but differentiable f(x) is neither continuous nor differentiable