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Evaluate: lim(xto1)(x^(x)-1)/(xlogx)...

Evaluate:
`lim_(xto1)(x^(x)-1)/(xlogx)`

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CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-CALCULUS
  1. Evaluate: lim(xto2)(sqrt(2x+5)-3(sqrt(2x-3)))/(root3(2x-3))

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  2. Evaluate: lim(xto0)(1+sin2x)^(cosecx)

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  3. Evaluate: lim(xto1)(x^(x)-1)/(xlogx)

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  4. Evaluate: lim(xto0)(log(1+x+x^(2))+log(1-x+x^(2)))/(secx-cosx)

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  5. Prove that lim(xto0)(xsqrt(2ax-x^(2)))/((sqrt(8ax-4x^(2))+sqrt(8ax))^(...

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  6. Evaluate [without using L' Hospital's rule]: lim(xto2)(2-sqrt(2+x))/...

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  7. Evaluate [without using L' Hospital's rule]: lim(xto(pi)/(4))(4sqrt2...

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  8. Find the differential coefficient of: cos(ax^(2)+bx+c)

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  9. Find the differential coefficient of: tan^(2)(ax)

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  10. Find the differential coefficient of: x^(x)

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  11. Find from first principle the differential coefficient of: xtan^(-1)...

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  12. Examine the differentiability of f(x)=|sinx-cosx|" at "x=(pi)/(4)

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  13. Prove that the function f(x)=|x| is not differentiable there at x=0.

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  14. Let f(x)=2x+3" " for xle1 =ax^(2)+bx" " for xgt1 If...

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  15. If f(2)=4,g(2)=9andf'(2)=2g'(2), then evaluate lim(xto2)(sqrt(f(x))-2)...

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  16. If f(9)=9,f'(9)=4, then evaluate lim(xto9)(sqrtf(x)-3)/(sqrtx-3).

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  17. Let f((x+y)/(2))=(1)/(2)[f(x)+f(y)] for all real x and y. If f'(0) exi...

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  18. If f(x) is differentiable at x=a, find the value of lim(xtoa)((x+a)f(x...

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  19. The value of lim(xto0)f(x) where f(x)=(x^(3)+x^(2))/(2x^(3)-27x^(2))

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  20. If f(x+y)=f(x)f(y) for all x, y and f(x)=1+xg(x), where lim(xto0)g(x)=...

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