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Evaluate the following limits : lim(nra...

Evaluate the following limits :
`lim_(nrarrinfty)(1^2+2^2+3^2+...+n^2)/(2n^3)`

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PATHFINDER-LIMIT, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. Number of point of discontinuity of f(x)=tan^2x-sec^2x in (0, 2pi) is

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  2. Evaluate the following limits : lim(xrarr0)(5^x-4^x)/(3^x-1)

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  3. Evaluate the following limits : lim(nrarrinfty)(1^2+2^2+3^2+...+n^2)/...

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  4. Evaluate the following limits : lim(xrarrpi/2)(sec x-tan x)

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  5. Evaluate the following limits : lim(xrarrinfty)(x-sqrt(x^2+ x))

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  6. Evaluate the following limits : lim(xrarr0)sqrt((1/2(1-cos2x))/x

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  7. Evaluate the following limits : lim(xrarr0)(1+|sinx|)^(1/x)

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  8. Evaluate the following limits : lim(xrarr1)(1-x)tan frac(pix)2

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  9. Evaluate the following limits : lim(xrarrinfty)x(e^(1/x)-1)

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  10. Evaluate the following limits : lim(xrarrpi/3)sin(pi/3-x)/(2cosx-1)

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  11. Evaluate the following limits : lim(nrarrinfty)n(x^(1/n)-1), xgt0

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  12. Find the set of points where the following functions are discontinuous...

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  13. Find the set of points where the following functions are discontinuous...

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  14. Find the set of points where the following functions are discontinuous...

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  15. Find the set of points where the following functions are discontinuous...

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  16. Find the set of points where the following functions are discontinuous...

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  17. Find the set of points where the following functions are discontinuous...

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  18. Let f(x) = {((x^2-4)/(x+2), x lt -3), (Ina, x=-3), (a+bx, x gt -3):}. ...

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  19. Let f(x) = {(ax+1, x lt 1), (3, x=1), (bx^2+1, x gt 1):}. For what val...

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  20. Let f be a twice differentiable function such that f"(x) = -f(x) , and...

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