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Let f (x)= {{:(x ^(n) (sin ""(1)/(x )","...

Let `f (x)= {{:(x ^(n) (sin ""(1)/(x )",") , x ne 0),( 0"," , x =0):}` Such that f (x) is continuous at `x =0, f '(0)` is real and finlte, and `lim _(x to 0^(+)) f'(x)` does not exist. The holds true for which of the following values of n ?

A

0

B

1

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
C
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VK JAISWAL-CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION-EXERCISE (SUBJECTIVE TYPE PROBLEMS)
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  3. If y= sin (8 sin ^(-1) x ) then (1-x ^(2)) (d^(2)y)/(dx ^(2))-x (dy)/...

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  4. If y ^(2) =4ax, then (d^(2) y)/(dx ^(2))=(ka ^(2))/( y ^(2)), where k ...

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  5. The number of values of x , x I [-2,3] where f (x) =[x ^(2)] sin (pix)...

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  6. If f (x) is continous and fifferentiable in [-3,9] and f'(x) in [-2,8]...

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  7. In f (x)= [{:(cos x ^(2),, x lt 0), ( sin x ^(3) -|x ^(3)-1|,, x ge 0)...

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  8. Let f (x) =x ^(2) +ax+3 and g (x) =x+b, where F (x) =lim (xto oo) (f(x...

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  13. f (x) =a cos (piy)+b, f'((1)/(2))=pi and int (1//2)^(3//2) f (x) dx =2...

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  14. Let alpha (x) = f(x) -f (2x) and beta (x) =f (x) -f (4x) and alpha '(1...

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  15. Let f (x) =-4.e ^((1-x)/(2))+ (x ^(3))/(3 ) + (x ^(2))/(2)+ x+1 and g ...

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  16. If y=3^(2 sin ^(-1)) then |((x ^(2) -1) y ^(+) +xy')/(y)| is equal to

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  17. Let f (x)=x+ (x ^(2))/(2 )+ (x ^(3))/(3 )+ (x ^(4))/(4 ) +(x ^(5))/(5)...

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  18. In f (x)= [{:(cos x ^(2),, x lt 0), ( sin x ^(3) -|x ^(3)-1|,, x ge 0)...

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  19. Let f :R to R be a differentiable function satisfying: f (xy) =(f(x)...

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  20. For the curve sin x + si y=1 lying in the first quadrant there exist a...

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  21. Let f (x) = x tan ^(-1) (x^(2)) + x^(4) Let f ^(k) (x) denotes k ^(th)...

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