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If underset(xrarroo)(lim)xlog(e)(|(alpha...

If `underset(xrarroo)(lim)xlog_(e)(|(alpha//x,1,gamma),(0,1//x,beta),(1,0,1//x)|)=-5.` where `alpha, beta, gamma` are finite real numbers, then

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CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. If y=(sin^(-1)x)/(sqrt(1-x^2)),t h e n(1-x^2)(dy)/(dx) is equal to (a)...

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  2. If (lim)(xvec0)(a e^x+bcos x+c e^(-x))/(e^(2x)-2e^x+1)=4,t h e n a.a=...

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  3. If underset(xrarroo)(lim)xlog(e)(|(alpha//x,1,gamma),(0,1//x,beta),(1,...

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  4. Evaluate: (lim)(x->(3pi)/4)(1+(tanx)^(1/3))/(1-2cos^2x)

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  5. Let f : R rarr R be a differentiable function at x = 0 satisfying f(0)...

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  6. (lim)(xvec0^+)1/(xsqrt(x))("a t a n"^(-1)(sqrt(x))/a-btan^(-1)(sqrt(x)...

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  7. If f^(prime)(a)=1/4, t h e n(lim)(hvec0)(f(a+2h^2)-f(a-2h^2))/(f(a+h^3...

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  8. The value of lim(x->0)(e^(x^2)-e^x+x)/(1-cos2x) is

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  9. Evalaute underset(xto1)lim(1+logx-x)/(1-2x+x^(2))

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  10. The value of lim(x->1)(x ^(1/13)-x^(1/7))/((x^(1/5) - x^(1/3)) is (44)...

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  11. If f(x)={x/(s in x),x >0 2-x ,xlt=0 and g(x)={x+3,x<1x^2-2x-2,1lt=x<2x...

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  12. If k in I sucht that (lim)(xvecoo)("cos"(kpi)/4)^(2n)-(cos-(kpi)/6)^(...

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  13. underset(xrarroo)(lim)(sum(r=1)^(10)(x+r)^(2010))/((x^(1006)+1)(2x^(10...

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  14. If underset(xrarr0)(lim)(f(x))/(x^(2))=aand underset(xrarr0)(lim)(f(1-...

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  15. The value of lim(x->pi/4)(tan^3x-t a n x)/(cos(x+pi/4)) is 8 b. -4 c. ...

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  16. (lim)(xvecpi/2)((1-sin x)(8x^3-pi^3)cos x)/((pi-2x)^4) a.(pi^2)/6 b...

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

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  18. The value of (lim)(x->oo)(e^sqrt(x^(4+1))-e^(x^(2+1))) is (a) 0 b. e c...

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  19. If an and bn are positive integers and an+sqrt(2)bn=(2+sqrt(2))^n ,t h...

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  20. Iff(x)={x+1/2, x&lt;0 2x+3/4,x &gt;=0 , then [(lim)(x-&gt;0)f(x)]= (...

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