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Let f (x) = {{:( -3 "," , - 3 le x lt 0 ...

Let `f (x) = {{:( -3 "," , - 3 le x lt 0 ), ( x ^(2) - 3 "," , 0 lt x le 3 ):} and g (x) = |f (x) |+f (|x|),` then which of the following is true ?

A

at `x =0 , g (x)` is continuous as well as differentiable

B

`at x = sqrt3, g (x)` is continuous but not differentiable

C

`at x =2, g (x)` is neither continuous nor differentiable

D

None of these

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The correct Answer is:
A, B
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MTG-WBJEE-DERIVATIVES -WB JEE PREVIOUS YEARS QUESTIONS
  1. Let f (x) = {{:( -3 "," , - 3 le x lt 0 ), ( x ^(2) - 3 "," , 0 lt x l...

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  2. Let f (x) = {{:( x ^(2) - 3x + 2 "," , x lt 2 ), ( x ^(3) - 6x ^(2) + ...

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  3. Let f(x) = asin|x| + be^|x| is differentiable when

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  4. Let R be the set of all real number and f: [-1,1] to R is difined by ...

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  5. Suppose that f (x) is a differentiable function such that f'(x) is con...

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  6. For all real values of a (0) , a (1), a (2), a (3) satisfying a (0)+ (...

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  7. If y=(1+x)(1+x^2)(1+x^4)(1+x^(2n)), then find (dy)/(dx)a tx=0.

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  8. If y=f(x) is an odd differentiable function defined on (-oo,oo) such ...

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  9. If f (x) = tan ^(-1) [ (log ((e )/( x ^(2))))/(log (ex ^(2)))] + tan ^...

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  10. Consider the non-constant differentiable function f of one variable wh...

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  11. if f(x)=log5 log3 x then f'(e) is equal to

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  12. Let F (x) = e ^(x) , G (x) =e ^(-x) and H (x) = G (F(x)), where x is a...

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  13. IF y = e ^(m sin ^(-1)x)) and (1- x ^(2)) (d ^(2) y )/( dx ^(2)) - x ...

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  14. Let f (x) = {{:((x ^(p))/(( sin x ) ^(q) )"," , 0 lt x le (pi)/(2) ), ...

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  15. For all twice differentiable functions f : R to R , with f(0) = f...

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  16. Let f1(x)=e^x,f2(x)=e^(f1(x)),......,f(n+1)(x)=e^(fn(x)) for all n>=1....

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  17. Let f : [a,b] to Rbe differentiable on [a,b]& k in R. Let f (a) =0 = f...

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  18. Let f (x) gt 0 for all x and f'(x) exists for all x. If f is the inver...

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  19. Applying Largrange's mean value theorem for a suitable function f (x) ...

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  20. The number of points at which the function f(x) = max{a - x, a + x, b}...

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  21. Let f be arry continuously differentiable function on [a,b] and twice ...

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