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If f(x)={{:(,(x log cos x)/(log(1+x^(2))...

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

A

f(x) is not continous at x=0

B

f(x) is continuous at x=0

C

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

D

`f(x)` is differentiable at x=0.

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The correct Answer is:
B, D
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ML KHANNA-LIMITS, CONTINUITY AND DIFFERENTIABILITY -PROBLEM SET (2) (MULTIPLE CHOICE QUESTIONS)
  1. Let [x] denotes the greatest integer less than or equal to x. If f(x) ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  17. If for a continuous function f,f(0)=f(1)=0,f^(prime)(1)=2a n dy(x)=f(e...

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  18. The function f(x) = e^(|x|) is

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  19. Let f(x) be defined as f(x) = {{:(sin 2x, 0 lt x lt pi/6),(px + q, p...

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  20. Let f(x) = {{:(-1/|x|, "for " |x| ge 1),(ax^(2)-b, "for " |x| lt 1):},...

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