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Evaluate: lim(x->a)("log"(x-a))/(log(e^x...

Evaluate: `lim_(x->a)("log"(x-a))/(log(e^x-e^a))`

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CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. Evaluate: lim(x->0)(a^(tanx)-a^(sinx))/(tanx-sinx),a >0

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  2. lim(x->oo)((2x+1)^(40)(4x-1)^5)/((2x+3)^(45)) is equal to (a)16 ...

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  3. Evaluate: lim(x->a)("log"(x-a))/(log(e^x-e^a))

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  4. The value of underset(xto2)lim(sqrt(1+sqrt(2+x))-sqrt(3))/(x-2)" is "

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

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  6. lim(n->oo)n^2(x^(1/n)-x^(1/((n+1)))),x >0 , is equal to (a)0 (b) e^x ...

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  7. Evaluate: ("lim")(xtooo)x^(1/x)

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  8. The value of lim(x->pi)(1+cos^3x)/(sin^2x) is (a)1/3 (b) 2/3 ...

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  9. Evaluate: underset(x rarr 0)("lim") ((729)^x-(243)^x-(81)^x+9^x+3^x-1...

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  10. If f(x)=(3x^2+a x+a+1)/(x^2+x-2), then which of the following can be c...

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  11. Evaluate underset(ntooo)lim(-1)^(n-1)sin(pisqrt(n^(2)+0.5n+1)),"where ...

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  12. ("lim")(ntooo)1/(1+nsin^2n x) is equal to (a)-1 (b) 0 (c) 1 (d) ...

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  13. Let the sequence ltb(n)gt of real numbers satisfy the recurrence relat...

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  14. Which of the following true ({.} denotes the fractional part of the ...

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  15. Evaluate: lim(n->oo)(4^n+5^n)^(1/n)

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  16. If ("lim")(x->1)(2-x+a[x-1]+b[1+x]) exists, then a and b can take the ...

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  17. Evaluate lim(ntooo) (n^(p)sin^(2)(n!))/(n+1),"where "0ltplt1.

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  18. If lim(nrarrinfty)(an-frac(1+n^2)(1+n))=b a finite number then

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  19. Evaluate underset(xtooo)limx^(3){sqrt(x^(2)+sqrt(1+x^(4)))-xsqrt(2)}.

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  20. prove that, If m , n in N ,("lim")(xto0)(sinx^n)/((sinx)^m)i s (a) 1,...

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