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Evaluate: underset(x rarr 0)("lim") ((7...

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

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CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. Evaluate: ("lim")(xtooo)x^(1/x)

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

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

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

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

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

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

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

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

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

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

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

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

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  15. For any two complex numbers z1,z2 and any real numbers <math xmlns="ht...

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  16. lim(n->oo)(-3n+(-1)^n)/(4n-(-1)^n) is equal to a. -3/4 b. 0 if n is...

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  17. Evaluate underset(xtooo)lim(sqrt(25x^(2)-3x)+5x).

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  18. Given a real-valued function f such that f(x)={(tan^2{x})/((x^2-[x]^2)...

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  19. Evaluate underset(xtooo)lim((x^(2)+x-1)/(3x^(2)+2x+4))^((3x^(2)+x)/(x-...

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  20. L=lim(x to a)(|2sinx-1|)/(2sinx-1)dotT h e n (a) limit does not exis...

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