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If (x^(2)+x-2)/(x+3)le(f(x))/(x^(2))le(x...

If `(x^(2)+x-2)/(x+3)le(f(x))/(x^(2))le(x^(2)+2x-1)/(x+3)` holds for a certain interval containing the value of `underset(xto-1)limf(x).`

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CENGAGE PUBLICATION-LIMITS AND DERIVATIVES-All Questions
  1. Evaluate the following limits using sandwich theorem: lim(x->oo)([x])...

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  2. lim(x->0) (sinx^n)/((sinx)^m),(mltn), is equal to (a) 1 (b) 0 (c) n...

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  3. If (x^(2)+x-2)/(x+3)le(f(x))/(x^(2))le(x^(2)+2x-1)/(x+3) holds for a c...

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  4. lim(x->oo)(2sqrt(x)+3root3x+4root4x+.......+nrootnx)/(sqrt((2x-3))+roo...

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  5. Let f:(1,2)vecR satisfies the inequality (cos(2x-4)-33)/2ltf(x)lt(x^2|...

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  6. lim(y->0)((x+y)sec(x+y)-xsecx)/y is equal to (a) secx(xtanx+1) (b) x...

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  7. Evaluate underset(ntooo)lim(1)/(1+n^(2))+(2)/(2+n^(2))+...+(n)/(n+n^(2...

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  8. If L=lim(x->2) ((10-x)^(1/3) -2)/(x-2), then the value of |1/(4L)| ...

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  9. Suppose that f is a function such that 2x^2lt=f(x)lt=x(x^2+1) for all ...

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  10. If L=lim(xto0) (e^(-x^(2)//2)-cosx)/(x^(3)sinx), then find the value o...

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  11. If [dot] denotes the greatest integer function, then find the value of...

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  12. If lim(x->oo) f(x) exists and is finite and nonzero and if lim(x->oo)...

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  13. If 3-((x^(2))/(12))lef(x)le3+((x^(3))/(9)) in the neighborhood of x=0,...

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  14. If f(x)={{:(x-1", "xge1),(2x^(2)-2", "xlt1):},g(x)={{:(x+1", "xg...

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  15. Evaluate underset(xto0)lim{(sinx-x+(x^(3))/(6))/(x^(5))}.

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  16. underset(xtooo)limf(x)," where "(2x-3)/(x)ltf(x)lt(2x^(2)+5x)/(x^(2))A...

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  17. Evaluate underset(xto0)lim(sinx+log(1-x))/(x^(2)).

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  18. If underset(xto0)lim[1+x+(f(x))/(x)]^(1//x)=e^(3), then the value of l...

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  19. Evaluate the limits using the expansion formula of functions lim(x->0)...

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  20. The value of ("lim")(n->oo)[(n+1)^2 3-(n-1)^2 3] is

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