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let f(x)=(cos^-1(1-{x})sin^-1(1-{x}))/sq...

let `f(x)=(cos^-1(1-{x})sin^-1(1-{x}))/sqrt(2{x}(1-{x}))` where `{x}` denotes the fractional part of `x` then

A

`lim _(x to 0^(+))f (x)= (pi)/(4)`

B

`lim _(x to 0^(+))f (x) =sqrt2 lim _(x to 0^(-))f (x)`

C

`lim _(x to 0^(-))f (x) =(pi)/(4 sqrt2)`

D

`lim _(x to 0^(-))f (x) = (pi)/(2 sqrt2)`

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B, D
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VIKAS GUPTA (BLACK BOOK)-LIMIT-EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)
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  6. lim(x->0) (sin(sinx)-sinx)/(ax^3+bx^5+c)=-1/12 then

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  7. If f (x) = lim ( n to oo) (n (x ^(1//n)-1)) for x gt 0, then which of...

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  8. lim(n->oo)cos^2(pi(3sqrt(n^3+n^2+2n)-n)) where n is an integer,equals

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  12. Let f (x)= [{:(x+3,, -2 lt x lt 0),(4, x=0),(2x+5,, 0 lt x lt 1):}, t...

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  13. Let f (x)= [{:(x+3,, -2 lt x lt 0),(4, x=0),(2x+5,, 0 lt x lt 1):}, t...

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  14. A certain function f(x) has the property that f(3x)=alpha f(x) for all...

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  15. A certain function f (x) has the property that f (3x)=alpha f (x) for ...

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  16. Consider the limit lim (x to 0) (1)/(x ^(3))((1)/(sqrt(1+x))- ((1+ ax)...

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  17. Consider the limit lim (x to 0) (1)/(x ^(3))((1)/(sqrt(1+x))- ((1+ ax)...

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  18. Consider the limit lim (x to 0) (1)/(x ^(3))((1)/(sqrt(1+x))- ((1+ ax)...

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  19. For the curve sinx+siny=1 lying in first quadrant. If underset(xrarr0...

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  20. Ror the curve sin x+ sin y=1 lying in the first quadrant there exists ...

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