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If f(x) = |sinx|, then...

If `f(x) = |sinx|`, then

A

differentiable everwhere

B

not differentiable at `x=n pin , in I`

C

not diffentiable at `x=0`

D

continous at `x=0`

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The correct Answer is:
A, D
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VIKAS GUPTA (BLACK BOOK) ENGLISH-CONTINUITY, DIFFERENTIABILITY AND DIFFERENTIATION-EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)
  1. Identify the options having correct statement:

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  2. A twice differentiable function f(x)is defined for all real numbers an...

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  3. If f(x) = |sinx|, then

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  4. Let [.] represent the greatest integer function and f (x)=[tan^2 x] th...

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  5. Let f be a differentiable function satisfying f'(x)=f' (-x) AA x in R....

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  6. Let f :R to R be a function, such that |f(x)|le x ^(4n), n in N AA n i...

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  7. Let f (x) =[x] and g (x) =0 when x is an integer and g (x) =x ^(2) whe...

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  8. let the function f be defined by f (x)= {{:(p+ qx+ x^(2)"," , x lt 2),...

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  9. Let f (x) =|2x-9|+|2x+9|. Which of the following are true ?

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  10. Let f (x)= max (x,x ^(2) x ^(3)) in -2 le x le 2. Then:

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  11. Let f(x) be a differentiable function satisfying f(y)f(x/y)=f(x) AA, x...

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  12. Let f(x) =(x^(2)-3x+ 2) (x ^(2) + 3x +2) and alpha, beta, gamma satisf...

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  13. Let f:RtoR is given by f(x)={(p+qx+x^(2),xlt2),(2px+3qx^(2),xge2):} t...

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  14. Let y=e^x s in x^3+(t a n x)^xdotF in d(dy)/(dx)dot

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  15. Let f(x)=x +(1-x) x ^(2) +[1- x) (1- x^(2)) +…..+ (1-x) …….(1-x ^(n-1)...

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  16. Let f (x)= [{:(x ^(2)+a,0 le x lt 1),( 2x+b,1le x le 2):}and g (x)=[{:...

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  17. If f(x) = {{:((sin[x^(2)]pi)/(x^(2)-3x - 18)+ax^(2)+b",","for",0 le x ...

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  18. Let f (x) [ {:(1+x"," , 0 le x le 2),( 3-x"," ,2 lt x le 3):}: g(x...

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  19. Let f (x)=(x+1) (x+2) (x+3)…..(x+100) and g (x) =f (x) f''(x) -f'(x) ...

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  20. Let f(x)={{:(,|x|-3,x lt 1),(,|x-2|+a,x ge 1):} g(x)={{:(,2-|x|,x lt...

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