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Evaluate the following limits : lim(nra...

Evaluate the following limits :
`lim_(nrarrinfty)n(x^(1/n)-1)`, `xgt0`

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PATHFINDER-LIMIT, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. Evaluate the following limits : lim(xrarrinfty)x(e^(1/x)-1)

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

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

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

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

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

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

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

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

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

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

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

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  13. If |c|le1/2 and f(x) is a differentiable function at x = 0 given by ...

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  14. Let f(x)={(x+a if x lt 0), (|x-1| if x ge 0):} and g(x)={(x+1 if x lt ...

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  15. f is a function such that f(x + y) = f(x) .f(y),forall x, y in R , if ...

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  16. A real valued function satisfies the relation f(x+y)=f(x)+f(y)+(e^x-1)...

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  17. If f(x)f(y) + 2 = f(x) + f(y) + f(xy) and f(1) = 2, f'(1) = 2, then fi...

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  18. Let f(x)={(1+x, 0 le x le 2), (3-x, 2 lt x lt 3):} Determine the for...

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  19. Let f(x)={(1+x, 0 le x le 2), (3-x, 2 lt x lt 3):} Discuss the conti...

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  20. Let f(x)={(x exp[-(1/|x|+1/x)], x ne 0),(0, x=0):} Test whether f(x)...

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