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Let g(x)=xf(x), where f(x)={{:(x^(2)sin....

Let `g(x)=xf(x)`, where `f(x)={{:(x^(2)sin.(1)/(x),":",x ne0),(0,":",x=0):}`. At `x=0`,

A

g is differentiable but g' is not continuous

B

g is differentiable while f is not differentiable

C

both f and g are differentiable

D

g is differentiable but g' is continuous

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The correct Answer is:
A, B
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ML KHANNA-LIMITS, CONTINUITY AND DIFFERENTIABILITY -PROBLEM SET (2) (MULTIPLE CHOICE QUESTIONS)
  1. The function f(x) is defined as: f(x) =1/3 -x, x ,lt 1/3 =(1/3-x)^...

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

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  3. Let g(x)=xf(x), where f(x)={{:(x^(2)sin.(1)/(x),":",x ne0),(0,":",x=0)...

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  4. Let f(x)={{:(0,x lt 0),(x^(2),xge0):}, then for all values of x

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  5. Let [x] denotes the greatest integer less than or equal to x. If f(x) ...

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

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  7. If f(x)={{:(,(x log cos x)/(log(1+x^(2))),x ne 0),(,0,x=0):} then

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  8. If x+4|y| = 6y then y as a function of x is

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  9. If f'(x(0)) exists, then lim(h to 0)([f(x(0) +h) -f(x(0) -h))/(2h)) is...

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  10. The function f(x) = {{:(|2x-3|[x], x ge 1),(sin((pix)/2), x lt 1):}

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  11. The function f (x) is defined as under : f(x)={{:(3^(x), -1 le x le...

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  12. A function is defined as follows : f(x) = {{:(x^(3), x^(2) lt 1),(x,...

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  13. The left-hand derivative of f(x) =[x]sin (pix) at k an interger, is:

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  14. If the derivative of the function f(x)={{:(ax^(2)+b,xlt-1),(bx^(2)+a...

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  15. If f(x) = {{:(ax^(2) + b, b ne 0, x le 1),(bx^(2) + ax + c,, x gt 1):}...

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  16. Let f(x) = a|x|^(2) + b|x| +c where a,b,c are real constants. Then f'(...

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  17. Let h(x) = "min" {x,x^(2)} , for every real number of x. Then

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  18. Let f : R to R be a function defined by f(x) = max. {x, x^(3)}. The s...

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  19. The derivative of f(x) =|x| at x = 0 is:

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  20. For a differentiable function f, the value of lim(h to 0) ([f(x+h)]^(2...

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