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Evaluate: ("lim")(xvec0)(2^x-1)/(sqrt(1+...

Evaluate: `("lim")_(xvec0)(2^x-1)/(sqrt(1+x)-1)`

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BANSAL-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. Evaluate the following limit: (lim)(x->0)(t a n2x-x)/(3x-sin x)

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  2. Evaluate: ("lim")(nvecoo)ncos(pi/(4n))sin(pi/(4n)) where (x , y)vec(0...

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  3. Evaluate: ("lim")(xvec0)(2^x-1)/(sqrt(1+x)-1)

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  4. Evaluate: ("lim")(xvec1)(a^(x-1)-1)/(sinpix)

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  5. Evaluate: ("lim")(xvec0)(10^x-2^x-5^x+1)/(xtanx)

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  6. Evaluate: ("lim")(xveca)(logx-loga)/(x-a)

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  7. Evaluate: ("lim")(xvec0)(log(5+x)-"log"(5-x))/x

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  8. Leg pn=a^(P(n-1))-1,AAn=2,3, ,a n dl e tP1=a^x-1, where a in R^+dot ...

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  9. Evaluate the following limit: (lim)(x->0)(e^(t a n x)-e^x)/(tanx-x)

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  10. Evaluate the following limit: (lim)(x->0)(a^(t a n x)-a^(s in x))/(...

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  11. Evaluate the following limit: (lim)(x->0)(e^x^2-cos^x)/(x^2)

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  12. Evaluate the following limit: (lim)(x->0)(e^(sin2x)-e^(sin\ x))/x

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  13. Evaluate the following limit: (lim)(x->0)(cos(x e^x)-"cos"(x e^(-x)...

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  14. Evaluate the following limit: (lim)(x->0)(e^1//x^2-1)/(2\ a r ctanx...

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  15. If (lim)(x->1)(pi/4-tan^(-1)\ \ x)/(e^("sin"(lnx))-x^n) exists and has...

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  16. Evaluate the following limit: (lim)(x->oo)(a^(1//x)-1)x

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  17. Evaluate the following limit: (lim)(x->0)(x(2^x-1))/(1-cos x)

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  18. Evaluate the following limit: (lim)(x->2)("sin"(e^(x-2)-1))/("log"(...

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  19. Evaluate the following limit: (lim)(x->0)(e^x^2-cos^x)/(x^2)

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  20. Evaluate the following limit: (lim)(x->0)(e^x+e^(-x)-2)/(x^2)

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