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

The function `f(x)=e^(-|x|)` is continuous everywhere but not differentiable at `x=0` (b) continuous and differentiable everywhere (c) not continuous at `x=0` (d) none of these

A

continuous everywhere but not differentiable at x=0

B

continuous and differentiable everywhere

C

not continuous at x=0

D

None of these

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OBJECTIVE RD SHARMA ENGLISH-CONTINUITY AND DIFFERENTIABILITY-Exercise
  1. Let f(x)=(x+|x|)|x| . Then, for all x f is continuous

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  2. The set of all points where the function f(x)=sqrt(1-e^(-x^2)) is di...

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  3. The function f(x)=e^(-|x|) is continuous everywhere but not differe...

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  4. The function f(x)=[cos x] is

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  5. If f(x)=sqrt(1-sqrt(1-x^2)) , then f(x) is (a) continuous on [-1, 1] ...

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  6. If f(x) = sin ^(-1)((2x)/(1 + x^(2))) then f (x) is differentiable in ...

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  7. about to only mathematics

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  8. If f(x)=|x-a|varphi(x), where varphi(x) is continuous function, then f...

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  9. If f(x)=x^2+(x^2)/(1+x^2)+(x^2)/((1+x^2)^2)+. . . . +(x^2)/((1+x^2)^n)...

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  10. If f(x)= | log10x| then at x=1.

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  11. If f(x)=|log(e) x|,then

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  12. If f(x)=|log(e)|x||," then "f'(x) equals

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  13. Let f(x)={1/(|x|)\ \ \ \ \ for\ |x|geq1a x^2+b\ \ \ \ \ \ \ \ for\ |x|...

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

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  15. If f(x)={(36^x-9^x-4^x+1)/(sqrt(2)-sqrt(1+cosx)),x!=0k ,x=0 is continu...

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  16. f(x)={|x - 4| for x leq 1 x^3/2-x^2+3x+1/2 for x lt 1 , then 1) ...

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  17. Let f(x) ={(sin2x , if 0leqxleqpi/6),(ax+b , if pi/6ltxlt1):} If f(x...

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  18. Let f(x)={(int(0)^(x){5+|1-t|}dt, "if" xlt2),(5x+1, "if" xge2):} then:

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  19. The function f defined by f(x)={{:(,(sinx^(2))/(x),x ne 0),(,0,x=0):} ...

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  20. If f(x) is continuous at x=0 and f(0)=2, then underset(x to 0)lim unde...

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