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

Evaluate: `lim_(x->0)(2^x-1)/((1+x)^(1/2)-1)`

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CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. Evaluate (lim(x->oo))(x(log)e{(sin(a+1/x))/(sina)}), 0 lt a lt pi/2

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  2. lim(x->0) {(1+x)^(2/x)} (where {.} denotes the fractional part of x ...

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  3. Evaluate: lim(x->0)(2^x-1)/((1+x)^(1/2)-1)

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  4. If f(n+1)=1/2{f(n)+9/(f(n))},n in N , and f(n)>0 for all n in...

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  5. Evaluate underset(xto1)lim(a^(x-1)-1)/(sinpix).

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  6. Find lim(x->0)(5x+2cosx)/(3x+14) using sandwitch theorem

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

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  8. If lim(n->oo)1/((sin^(-1)x)^("n")+1)=1 ,t h e n find the range of x.

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

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  10. Evaluate underset(xto0)lim(e^(x)-e^(xcosx))/(x+sinx).

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  11. Evaluate: lim(x->2)(x-2)/((log)a(x-1))

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  12. Evaluate: lim(x->0)(e^(sinx)-(1+sinx))/({tan^(-1)(sinx)}^2)

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  13. Evaluate: lim(x->a)(logx-loga)/(x-a)

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

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  15. Evaluate: lim(x->0)(10^x-2^x-5^x+1)/(xtanx)

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  16. lim(xto-1)((x^4+x^2+x+1)/(x^2-x+1))^((1-cos(x+1))/((x+1)^(2)) is equal...

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  17. Evaluate: lim(x->0)(3^(2x)-2^(3x))/x

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  18. lim(x->2)(((x^3-4x)/(x^3-8))^(-1)-((x+sqrt(2x))/(x-2)-(sqrt(2))/(sqrt(...

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  19. Evaluate: lim(x->0)(log(5+x)-"log"(5-x))/x

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  20. Each question contains statements given in two columns which have to b...

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