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f(x)=sqrt(1-sqrt(1-x^2) then at x=0 ,val...

`f(x)=sqrt(1-sqrt(1-x^2)` then at `x=0` ,value of f(x) is

A

continuous on [ -1,1] and differentiable on (-1,1)

B

continuous on [-1,1] and differentiable on `(-1,0) cup (0,1)`

C

continuous and differentiable on (-1,1)

D

Discontinuous on [-1,1]

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The correct Answer is:
B
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AAKASH INSTITUTE ENGLISH-CONTINUITY AND DIFFERENTIABILITY-Assignment ( section -A)
  1. If y = x^(1/x) , the value of (dy)/(dx) at x =e is equal to

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  2. If y = tan^(-1)( sqrt((x+1)/(x-1))) " for " |x| gt 1 " then " (dy)/(d...

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  3. If y="log"(2)"log"(2)(x), then (dy)/(dx) is equal to

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  4. If f'(x)= sqrt(2x^(2)-1) and y=f(x^(2)),then (dy)/(dx) at x = 1 is

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  5. Let the function f(x) be defined as f(x) = {:{((logx-1)/(x-e) , xnee),...

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  6. Rolle's theorem is not applicable to f(x) = |x| in [ -2,2] because

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  7. Lagrange's mean value theorem is not applicable to f(x) in [1,4] where...

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  8. The value of C ( if exists ) in Lagrange's theorem for the function |x...

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  9. If f be a function such that f(9)=9 and f'(9)=3, then lim(xto9)(sqrt(f...

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  10. If f(x) = {{:(1/(1+e^(1//x)), x ne 0),(0,x=0):} then f(x) is

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  11. f(x)=sqrt(1-sqrt(1-x^2) then at x=0 ,value of f(x) is

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  12. Domain of differentiations of the function f(x) = |x -2| cos x is

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  13. Let f(x) = (sin (pi [ x + pi]))/(1+[x]^(2)) where [] denotes the great...

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  14. If f(x)=x^2+(x^2)/(1+x^2)+(x^2)/((1+x^2)^2)+ ....oo term then at x=0,f...

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  15. Let f(x)={(|x+1|)/(tan^(- 1)(x+1)), x!=-1 ,1, x!=-1 Then f(x) is

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  16. The value of lim(h to 0) (f(x+h)+f(x-h))/h is equal to

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  17. If y = (e^(x)+1)/(e^(x)-1), " then" (y^(2))/2 + (dy)/(dx) is equal to

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  18. If f(x)=e^(x)g(x),g(0)=2,g'(0)=1, then f'(0) is

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  19. If ax^(2)+2hxy+by^(2)=0,"show that "(d^(2)y)/(dx^(2)) =0

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  20. Derivative of the function f(x) = log(5) (log(8)x), where x > 7 is

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