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Using L'Hospital 's rule prove that lim(...

Using L'Hospital 's rule prove that` lim_(theta rarr 0) (theta-sintheta)/(theta^3)=1/6`

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A DAS GUPTA-Limit, Indetermine Form-Exercise
  1. Using L'Hospital 's rule prove that lim(theta rarr 0) (theta-sintheta)...

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  2. lim(x rarr1)(sqrt(x^(2)+8)-sqrt(10-x^(2)))/(sqrt(x^(2)+3)-sqrt(5-x^(2)...

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  3. Evaluate: lim(xrarro) root(3)(1+x^2-1)/x^2

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  4. Evaluate: lim(xrarr0) ((1+x)^(1/3)-root(3)(1-sinx))/x

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  5. lim(x to 0) (root(3)(1+sin x)- root(3)(1-sinx))/x=

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  6. Evaluate the following limits : underset(xrarr0)"lim"(sqrt(cosx)-ro...

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  7. The value of lim(x rarr pi/4) sqrt(1 - sqrt(sin 2x))/(pi - 4x) is

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  8. Evaluate: ("lim")(xvecoo)x^3{sqrt(x^2+sqrt(1+x^4))-xsqrt(2)}

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  9. Evaluate: lim(xrarr -1)(x+1)/(root(4)(x+17)-2)

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  10. Evaluate: ("lim")(xvec0)(sin^(-1)x-tan^(-1)x)/(x^3)

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  11. Evaluate: lim(xrarr0) (2^x-9^x-3(x+1))/(sqrt2- sqrt1+cosx)

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  12. Find the limits: lim(x rarroo) ((x^2-2x+2)/(x^2-4x+1))^x

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  13. The value lim(xtopi//2)(sinx)^(tanx), is

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  14. Find the limits: lim(x rarr 0) (sin x/x)^(1/x)

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  15. Find the limits: lim(x rarr 0) (sin x +cos x)^(1/x)

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  16. Find the limits: lim(x rarr 0) (sec sqrt(x))^(10/x)

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  17. (lim)(x->1)(2-x)^(tan(pix)/2)

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  18. lim(x rarr 0+)(ln cotx)^(tanx)=

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  19. If f is derivable at x =a,then underset(xto a ) lim( (xf(a) -af( x))/...

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  20. lim(x rarr oo) (sqrt(x^2-x+1)-a x-b)=0, then a+b=

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  21. The value of lim(x->1) (x^n+x^(n-1)+x^(n-2)+....x^2+x-n)/(x-1) is

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