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

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  2. Evaluate: ("lim")(xvec0)(tanx)/x where [dot] represents the greatest ...

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

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  4. Evaluate: ("lim")(xvec2)(x-2)/((log)a(x-1))

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  5. Evaluate: lim(n->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")(xvec1)((x^4+x^2+x+1)/(x^2-x+1))^(1-"cos"(x+1))/((x+1)^(2))i se...

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

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  11. ("lim")(xvec2)(((x^3-4x)/(x^3-8))^(-1)-((x+sqrt(2x))/(x-2)-(sqrt(2))/(...

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  12. Evaluate: ("lim")(xvec0)(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 pn=a^(P(n-1))-1,AAn=2,3,... ,a n d l e tP1=a^x-1, where a in R^+...

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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) using sandwich theorem.

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  18. If f(x)={(x-|x|)/x ,x!=0, 2,x=0, show that lim(xrarr0) f(x) does not e...

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  19. The reciprocal of the value of: ("lim")(nvecoo)(1-1/(2^2))(1-1/(3^2))(...

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  20. Show that ("lim")(xrarr0) (e^(1/x)-1)/(e^(1/x)+1) does not exist

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