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If L=lim(x->oo){x-x^2(log)e(1+1/x)}, the...

If `L=lim_(x->oo){x-x^2(log)_e(1+1/x)},` then the value of `8L` is_____

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CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. Let Sn=1+2+3++n and Pn=(S2)/(S2-1)*(S3)/(S3-1)*(S4)/(S4-1)* . . . *...

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  2. If a(1)=1 and a(n+1)=(4+3a(n))/(3+2a(n)),nge1"and if" lim(ntooo) a(n)=...

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  3. If L=lim(x->oo){x-x^2(log)e(1+1/x)}, then the value of 8L is

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  4. Evaluate the limit: ("lim")(nrarroo)cos(pisqrt(n^2+n))when n is an in...

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  5. Evaluate: lim(x->a)(sqrt(a+2x)-sqrt(3x))/(sqrt(3a+x)-2sqrt(x)),(a!=0)...

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  6. Evaluate the limit: lim(x->0)(sqrt(2)-sqrt(1+cosx))/(sin^2x)

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  7. Let f ''(x) be continuous at x=0 If lim(xto0) (2f(x)-3af(2x)+bf(8x))...

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  8. Evaluate the limit: ("lim")(h -> 0)[1/(h(8+h)^(1/3))-1/(2h)]

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  9. Evaluate: lim(x->0)(e-(1+x)^(1/x))/x

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  10. Using lim(theta -> 0) (sintheta/theta)=1 prove that the area of circ...

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  11. Evaluate: lim(x->1)sec(pi/(2x))logxdot

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  12. Evaluate : [underset(x to 0)lim (sin x)/(x)], where [*] represents the...

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

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  14. Evaluate: lim(x->pi/2)(1+cos2x)/((pi-2x)^2)

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  15. Evaluate underset(ntooo)limn^(-n^(2))[(n+2^(0))(n+2^(-1))(n+2^(-2))......

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  16. Solve: lim(x->oo)2^(x-1) tan(a/(2^x))

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  17. Evaluate underset(xto pi//2)lim(sinx-(sinx)^(sinx))/(1-sinx+log(e)sinx...

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  18. Evaluate: lim(x->2)(x^2-x-2)/(x^2-2x-"sin"(x-2))

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  19. Evaluate: lim(x->0)(1/(x^2)-1/(sin^2x))

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  20. Evaluate: lim(x->oo)x(tan^(-1)((x+1)/(x+4))-pi/4)

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