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Let f(x)={((tan^(2){x})/(x^(2)-[x]^(2)),...

Let `f(x)={((tan^(2){x})/(x^(2)-[x]^(2)),"for"xgt0),(1/(sqrt({x}cot{x})),"for"xlt0):}` where `[x]` is the step up function and `{x}` is the fractional part function of x then

A

`lim_(xto^+)f(x)=1`

B

`lim_(xto0^-)f(x)=cot1 `

C

`cot^-1 (lim_(xto0^-) f(x))^2=1`

D

`tan^-1 (lim_(xto0^+)f(x))=(pi)/(4)`

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OBJECTIVE RD SHARMA ENGLISH-LIMITS-Exercise
  1. The value of underset(mtooo)lim("cos"(x)/(m))^(m) is

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  2. The value of lim(xrarroo)(sqrt(n^2+1)+sqrt(n))/((n^4+n)^(1/4)+4sqrt(n)...

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  3. The value of lim(xrarr0) (x^2sin((1)/(x)))/(sinx), is

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  4. If l=lim(xto-2) (tanpix)/(x+2)+lim(xtooo) ( (1+1)/(x^2)^2), then which...

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  5. The value of lim(nto oo)(sqrt(n^(2)+n+1)-[sqrt(n^(2)+n+1)]) where [.] ...

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  6. lim(xto oo) (1^2.n+2^2.(n-1)+3^2.(n-2)+......+n^2.1)/(1^3+2^3......+n^...

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  7. lim(x->oo)cot^(-1)(x^(-a)loga x)/(sec^(-1)(a^xlogx a)),(a >1)is equal ...

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  8. Let a= min { x^2+2x+3:x in R}and b=lim(x to0) (sin xcos x) /(e^x-e^-x...

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  9. underset(xrarroo)(lim)(cot^(-1)(sqrt(x+1)+sqrtx))/(sec^(-1){((2x+1)/(x...

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  10. Let f(x)=lim(nto oo) (2x^(2n) sin (1)/(x)+x)/(1+x^(2n)) , then which o...

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  11. Assume that underset(thetararr-1)(lim)f(theta) exists and (theta^(2)+t...

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  12. Let f(x)={((tan^(2){x})/(x^(2)-[x]^(2)),"for"xgt0),(1/(sqrt({x}cot{x})...

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  13. The integer n for which ("lim")(xvec0)((cosx-1)(cosx-ehatx)/(x^n) is f...

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  14. The value of lim(x->0) [x^2/(sin x tan x)] (Wherer [*] denotes grea...

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  15. underset(xto0)lim(x^(a)sin^(b)x)/(sin(x^(c))), where a,b,c inR~{0}, ex...

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  16. lim(xrarr2) ((10-x)^(1//3)-2)/(x-2) is equal to

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  17. If L=lim(x->0) (asinx-bx+cx^2+x^3)/(2x^2log(1+x)-2x^3+x^4) exists and ...

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  18. If alpha,beta are the roots of the equation ax^2+bx+c=0, then lim(xrar...

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  19. Find the integral value of n for which ("lim")(xvec0)(cos^2x-cosx-e^x...

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  20. The graph of function y=f(x) has a unique tangent at (e^(a),0) through...

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