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Evaluate lim(x rarr 1) ((x + x^2 + ........

Evaluate `lim_(x rarr 1) ((x + x^2 + .........+ x^n)-n)/(x - 1)`

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`(n(n+1))/2`
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A N EXCEL PUBLICATION-LIMITS AND DERIVATIVES-QUESTION BANK
  1. Find the value of a if lim(x rarr -a) (x^9 + a^9)/(x + a) = 9

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  2. What is the value of (lim(x rarr 1) (x^n - 1)/( x - 1) for any integer...

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  3. Evaluate lim(x rarr 1) ((x + x^2 + .........+ x^n)-n)/(x - 1)

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  4. Given that lim(theta rarr 0) (sin theta)/theta = 1 and lim(theta rarr ...

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  5. Given that lim(theta rarr 0) (sin theta)/theta = 1 and lim(theta rarr ...

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  6. Prove that (1 - cos 4theta)/(1 - cos 5theta) = [(sin (2theta))/(sin(5/...

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  7. Evaluate lim(theta rarr 0) (1-cos 4theta)/(1-cos 5theta)

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  8. Evaluate lim( x rarr a) (cos x - cos a)/(x -a)

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  9. Evaluate lim(x rarr a) (sqrtx - sqrta)/(x -a)

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  10. Evaluate lim(x rarr a) (cos x - cos a)/(sqrtx - sqrta)

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  11. If we assume u =tan^-1 2x, prove that lim(x rarr 0) x/(tan^-1 2x) = 1/...

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  12. Evaluate lim(x rarr 0) x/(tan^-1 2x)

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  13. Evaluate lim(x rarr pi/3)(sqrt3 - tan x)/(pi - 3x)

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  14. lim(x rarr 0) (tan x- sin x)/x^3

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  15. Evaluate lim(x rarr 0) (e^(bx) - 1)/x and lim(x rarr 0) (e^(ax) - 1)/x

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  16. Evaluate lim(x rarr 0) (e^(bx) - e^(ax))/x

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  17. What is the value of lim(x rarr pi/2) cos x ?

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  18. Evaluate lim(x rarr 0) (tan x)/x

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  19. Evaluate lim(x rarr 0) (3^x - 2^x)/(tan x)

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  20. Evaluate lim(x rarr 0) (log (1 + x/5))/x

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