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if f(x) ={{:( (x log cos x)/( log( 1+x^(...

`if f(x) ={{:( (x log cos x)/( log( 1+x^(2) )), x ne 0) ,( 0, x=0):}`

A

f(x) is not continuous at x=0

B

f(x) is continuous and differentiable at x=0

C

f(x) is continuous at x=0 but not differentiable at x=0

D

None of these

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OBJECTIVE RD SHARMA ENGLISH-CONTINUITY AND DIFFERENTIABILITY-Exercise
  1. Let f(x) be a function differentiable at x=c. Then underset(x to c)lim...

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  2. If (lim)(x->c)(f(x)-f(c))/(x-c) exists finitely, write the value of...

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  3. if f(x) ={{:( (x log cos x)/( log( 1+x^(2) )), x ne 0) ,( 0, x=0):}

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  4. The function f(x)=|x|+|x-1| is

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  5. For the function f(x)={{:(,|x-3|,x ge 1),(,(x^(2))/(4)-(3x)/(2)+(13)/(...

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  6. Let f(x)={{:(,x^(n)sin\ (1)/(x),x ne 0),(,0,x=0):} Then f(x) is contin...

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  7. If 4x+3|y|=5y, then y as a function of x is

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  8. If f(x)=x^3sgn(x), then

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  9. For a real number y, Let [y] denotes the geatest integer less than ...

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  10. If f(x)={{:(,x^(2)sin((1)/(x)),x ne 0),(,0, x=0):}, then

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  11. The following functions are differentiable on (-1,2)

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  12. If f(x)=sqrt(x+2sqrt(2x-4))+sqrt(x-2sqrt(2x-4)) then the value of 10 f...

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  13. The derivative of f(x)=|x|^(3) at x=0, is

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  14. If f (x) = x (sqrtx+sqrt((x+1)), then

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  15. Write the value of the derivative of f(x)=|x-1|+|x-3|"\ "a t"\ "x=3.

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  16. If f(x)=[x sin pix], then which of the following, is incorrect,

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  17. The function f(x)=1+|sin x|, is

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  18. If f(x)={{:(,1,x lt 0),(,1+sin x,0 le x lt (pi)/(2)):} then derivative...

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  19. Let [x] denotes the greatest integer less than or equal to x and f(x)=...

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  20. A function f : R to R satisfies the equation f(x+y) = f (x) f(y), AA ...

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