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Every continuous function is differentia...

Every continuous function is differentiable.

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Show that |x-5| is continuous but not differentiable at x =5.

Show that the function f(x) = {:{(x^n sin(1/x), x ne 0),(0, x = 0):} is continuous but not differentiable at x= 0.

Show that f(x) = |x - 5| is continuous but not differentiable at x = 5.

The function f(x) = |x| + |x-1| + |x-2| is continuous but not differentiable at for all x in R x=-1 and x=1

The function f(x)=sqrt(1-sqrt(1-x^2)) a. has its domain -1 le x le 1 b. has finite one sided derivates at the point x = 0 c. is continuous and differentiable at x = 0 d. is continuous but not differentiable at x = 0

Let alpha in R . Prove that a function f: RtoR is differentiable at alpha if and only if there is a function g:RtoR which is continuous at alpha and satisfies f (x) -f(alpha) = g (x) (x-alpha), AA x in R.

If f(x) = 3(2x + 3)^(2//3) + 2x + 3 , then: (a) f(x) is continuous but not differentiable at x = - (3)/(2) (b) f(x) is differentiable at x = 0 (c) f(x) is continuous at x = 0 (d) f(x) is differentiable but not continuous at x = - (3)/(2)

The composition of two continuous function is a continuous function.

Show that the function 'f' defined as follows, is continuous at x = 2, but not differentiable there at: f(x) = {:{(3x-2,0 2):}

if f(x) ={{:( (x log cos x)/( log( 1+x^(2) )), x ne 0) ,( 0, x=0):} a. f is continuous at x = 0 b. f is continuous at x = 0 but not differentiable at x = 0 c. f is differentiable at x = 0 d. f is not continuous at x = 0

PRADEEP PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. Fill in the blanks: If f(x) = x^(2//3), then f'(0) is ……… .

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  2. Fill in the blanks: Rolle's Theorem is not applicable to the functio...

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  3. Every continuous function is differentiable.

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  4. True or False : d/(dx) (logx) = 1/x for all x ne 0.

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  5. True or False : d/(dx) (log|x|) = 1/x for all x ne 0

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  6. If f is continuous on its domain D, then |f| is also continuous on D.

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  7. True or False : Rolle's Theorem is applicable to the function f(x) =...

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  8. Verify the truth of Rolle's Theorem for the following functions: f(X...

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  9. True or False : The function f(x) = log x^2 has only one point of di...

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  10. The composition of two continuous function is a continuous function.

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  11. true false: cos|x| is differentiable every where.

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  12. True or False : The function f(x) = {:{(x+a, xge1),(ax^2 +1, x <1):}...

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  13. True or False : The function f(x) = |sinx| is differetiable at all ...

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  14. Find ainR so that f(x) = {:{(x^2, x ge0),(ax,x<0):} is continuous at 0...

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  15. For continuity, at x=a, each of lim(xtoa^(+))f(x) and lim(xtoa^(-))f(x...

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  16. True or False : d/(dx) (log10x) = 1/x for all x >0

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  17. True or False : If underset(x rarr a)Lt f(x)g(x) exists then both un...

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  18. If f*g is continuous at x=a, then f and g are separately continuous at...

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  19. All trigonometric functions have inverse over their respective domains...

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  20. True or False : An increasing function is always a continuous functi...

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