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Evaluate underset(xto0)lim(e^(x)-e^(xcos...

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

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CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. If lim(n->oo)1/((sin^(-1)x)^("n")+1)=1 ,t h e n find the range of x.

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

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

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

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

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

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

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

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

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

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

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

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  14. Let P(n)=a^(P(n-1))-1,AA n=2,3,..., and let P(1)=a^(x)-1, where ainR^(...

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  15. Column I ([.] denotes the greatest integer function), Column II ""(...

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  16. Let f(x)={x+1,x >0, 2-x ,xlt=0 and g(x)={x+3,x<1,x^2-2x-2,1lt=x<2, ...

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  17. Evaluate: lim(x->oo) (x+7sinx)/(-2x+13)

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  18. Find the values of b for which the points (2b+3, b^(2)) lies above of ...

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  19. If f(x)={{:((x-|x|)/(x)","xne0),(2", "x=0):},show that underset(xt...

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  20. The reciprocal of the value of: lim(n->oo)(1-1/(2^2))(1-1/(3^2))(1-1/(...

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