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If f(x)=(lim)(nvecoo)(cos(x/(sqrt(n))))^...

If `f(x)=(lim)_(nvecoo)(cos(x/(sqrt(n))))^n` , then the value of `(lim)(xvec0)(f(x)-1)/x` is `0` b. `1` c. 2 d. `3//2`

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CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. lim(x->0)(e^(5x) - 1)/(3x)

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  2. lim(x->(pi/2)) (1-sinx)tanx =

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  3. The value of lim(x->3)((x^3+27)(log)e(x-2))/(x^2-9) is a. 9 b. 18 c....

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  4. If (lim)(xvec0)(e^(a x)-e^x-x)/(x^2)=b (finite), then a=2,b=0 b. a=0,b...

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  5. If underset(xrarr0)(lim)(x^3)/(sqrt(a+x)(bx-sinx))=1,agt0, then a+b is...

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  6. underset(xrarr0)(lim)[(sin^(-1)x)/(tan^(-1)x)]= (where [.] denotes the...

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  7. The value of lim(x->pi/4) (sqrt(1-sqrt(sin2x)))/(pi-4x) is

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  8. lim(x->0) (sin x /x)

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  9. If f(x)=x((e^(|x|+[x])-2)/(|x|+[x])) then (where [.] represents the gr...

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  10. If A=underset(xrarr0)(lim)(sin^(-1)(sinx))/(cos^(-1)(cosx))and B=under...

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  11. Let f(x)=lim(m->oo){lim(n->oo)cos^(2m)(n !pix)}, where x in Rdot Then...

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  12. lim(x->oo ){(e^x+pi^x)^(1/x)}= where {.} denotes the fractional par...

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  13. Let f(x)=(lim)(xvecoo)(tan^(-1)(tanx))/(1+((log)e x)^n),x!=(2n+1)pi/2 ...

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

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  15. lim(n->oo) ((sqrt(n^2+n)-1)/n)^(2sqrt(n^2+n)-1)

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  16. Let f: RvecR be such that f(a)=1,f^(prime)(a)=2. Then (lim)(xvec0)((...

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  17. If f(n)=underset(xto0)lim{(1+"sin"(x)/(2))(1+"sin"(x)/(2^(2)))...(1+"s...

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  18. If a >0,b >0 then (lim)(n->oo)((a-1+b^(1/n))/a)^n= b^(1//a) b. a^...

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  19. (lim)(xvec0)("log"(e^x^2+2sqrt(x)))/(t a nsqrt(x)) is equal to 0 b. 1 ...

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  20. If f(x)=(lim)(nvecoo)(cos(x/(sqrt(n))))^n , then the value of (lim)(xv...

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