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Let f : R rarr R be a differentiable fun...

Let `f : R rarr R` be a differentiable function at x = 0 satisfying f(0) = 0 and f'(0) = 1, then the value of `underset(x rarr 0)(lim) (1)/(x) . underset(n = 1)overset(oo)(sum)(-1)^(n).f((x)/(n))`, is

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CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
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  2. Evaluate: (lim)(x->(3pi)/4)(1+(tanx)^(1/3))/(1-2cos^2x)

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

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

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

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

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

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

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

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

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

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

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

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  18. 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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  19. (lim)(X-> (-7)([x]^2+15[x]+56)/("sin"(x+7)"sin"(x+8))= (where [.] deno...

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  20. Let L1=(lim)(x^vec4)(x-6)^x and L2=(lim)(x^vec4)(x-6)^4dot Which of t...

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