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If f(x)={{:(,1,x lt 0),(,1+sin x,0 le x ...

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

A

1

B

0

C

`infty`

D

does not exist

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Verified by Experts

The correct Answer is:
D
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TARGET PUBLICATION-DIFFERENTIATION -COMPETITIVE THINKING
  1. If f(x)={{:(,1,x lt 0),(,1+sin x,0 le x lt (pi)/(2)):} then derivative...

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  2. If f:R to R is defined by f(x)={{:(,(x-2)/(x^(2)-3x+2),"if "x in R-(1,...

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  3. If f(x) = {:{((x -1)/(2x^(2) - 7 x +5) , " for " x ne 1) , (-1/3 ...

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

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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. If f(x) = x for x le 0 = 0 for x gt 0, then f(x) at x = 0 is

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  7. At the point x = 1 , then function f(x) = {{:(x^(3) - 1, 1lt x lt o...

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  8. Define f(x) = {{:(x^(2)+bx+c , ",",x lt 1),(x,",",x ge 1):}. If f(x) i...

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  9. If f is differentiable at x=1, Then lim(x to1)(x^2f(1)-f(x))/(x-1) is

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  10. if f(2)=4,f'(2)=1 then lim(x->2){xf(2)-2f(x)}/(x-2)

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  11. If f(x) is differentiable at x=a, then lim(x toa)(x^2f(a)-a^2f(x))/(x-...

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  12. Suppose f(x) is differentiable at x = 1 and lim(h->0) 1/h f(1+h)=5, th...

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

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  14. Let g(x) = (x-1)^n/(log(cos^m(x-1))) ; 0 lt x lt 2 ,m and n and let p ...

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  15. Let f(x)={x^2|(cos)pi/x|, x!=0 and 0,x=0,x in RR, then f is

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  16. If the function g(x) = {(ksqrt(x+1) " when " 0 le x le 3),(mx + 2 " ...

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  17. Let S={t in R: f(x)=|x-pi|(e^(|x|)-1)sin|x| is not differentiable at t...

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  18. If y=cos (2x +45^(@) ),then (dy)/(dx) =

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  19. If y=sqrtsinsqrtx, then (dy)/(dx) =

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  20. d/(dx)log|x|e=

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