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Assume that underset(thetararr-1)(lim)f(...

Assume that `underset(thetararr-1)(lim)f(theta)` exists and `(theta^(2)+theta-2)/(theta+3)le(f(theta))/(theta^(2))le(theta^(2)+2theta-1)/(theta+3)` holds for certain interval containing the point `theta=-1 " then "underset(thetararr-1)(lim)f(theta)`

A

equal to `f(-1)`

B

equal to 1

C

non-existant

D

equal to `-1`

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A
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OBJECTIVE RD SHARMA ENGLISH-LIMITS-Exercise
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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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