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

If `f(x)=|log_(e)|x||," then "f'(x)` equals

A

f(x) is continuous and differentiable for all x in its domain

B

f(x) is continuous for all x in its domain but not differentiable at `x= pm1`

C

f(x) is neither continuous nor differentiable at `x= pm1`

D

None of these

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OBJECTIVE RD SHARMA ENGLISH-CONTINUITY AND DIFFERENTIABILITY-Exercise
  1. If f(x)= | log10x| then at x=1.

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

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

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

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

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  6. 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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  7. 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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  8. Let f(x) ={(sin2x , if 0leqxleqpi/6),(ax+b , if pi/6ltxlt1):} If f(x...

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

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

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

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  12. If f(x) defined by f(x)={(|x^2-x|)/(x^2-x1,x=0),x!=0,1-1,x=1 then (...

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  13. If f(x)={(1-sinx)/((pi-2x)^2)dot(logsinx)/((log(1+pi^2-4pix+4x^2))),x...

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  14. The set of points of differentiable of the function f(x)={{:(,(sqrt(x+...

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  15. The set of points where the function f(x)=|x-1|e^(x) is differentiable...

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  16. If f(x)=(x+1)^(cotx) be continuous at x=0, the f(0) is equal to

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  17. If f(x)={{:(,(sqrt(x+1)-1)/(sqrtx),"for "x ne 0),(,0,"for x=0):} and f...

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  18. The function f(x)={(e^(1/x)-1)/(e^(1/x)+1),x!=0 0,x=0 is continuous a...

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  19. Let f(x) ={{:((x-4)/(|x-4|)+a,xlt4),(a+b,x=4),( (x-4)/(|x-4|)+b, x gt4...

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  20. If the function f(x)={(cosx)^(1/x),x!=0k ,x=0 is continuous at x=0 , t...

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