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Evaluate the following limit: (lim)(x...

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

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BANSAL-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. Evaluate the following limit: (lim)(x->oo)(a^(1//x)-1)x

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

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

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

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

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  6. Evaluate the following limit: (lim)(x->a)(log(x-a))/("log"(e^x-e^a))

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  7. Evaluate the following limit: (lim)(x->0)(a^(t a n x)-a^(sin x))/(t ...

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  8. Evaluate: ("lim")(xvec0)((1-3^x-4^x+12^x))/(sqrt((2cosx+7)-3))

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  9. Evaluate: ("lim")(xvec0)((729)^x-(243)^x-(811)^x+9^x+3^x-1)/(x^3)

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  10. Evaluate: ("lim")(xvec0)(1+x)^(os e cx c)

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  11. Evaluate (lim)(x->0)(cos x)^(cos2\ x)

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  12. Evaluate ("lim")(xvec0)((sinx)/x)^(((sinx)/(x-sinx)))

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  13. Evaluate (lim)(x->0)((a^x+b^x+c^x)/3)^(2//x);(a ,\ b ,\ c >0)dot^(\...

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  14. Evaluate the following limits: (lim)(x->oo)((x-1)/(x+1))^(x+3)

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  15. Evaluate the following limits: (lim)(x->oo)((x+6)/(x+1))^(x+4)

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  16. Evaluate the following limits: (lim)(x->oo)(1+1/(a+b x))^(c+dx)w h ...

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

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  18. (lim)(x->oo)(sin(1/x)+cos(1/x))^x

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  19. (lim)(x->0)[tan(pi/4+x)]^(1/x)

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  20. (lim)(x->0)((1-t a n x)/(1+sin x))^(cos e c\ x)

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