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Evaluate: underset(x rarr 0)(lim) x^(sin...

Evaluate: `underset(x rarr 0)(lim) x^(sin x)`

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PREMIERS PUBLISHERS-APPLICATIONS OF DIFFERENTIAL CALCULUS-Problems For Practice (Answer the following question)
  1. Verify mean value theorem for the function f(x) = x^(3) - 5x^(2) 2x i...

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  2. Expand f(x) = e^(3x) on a maclaurin's series

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  3. Evaluate: underset(x rarr 2)(lim) (sin pi x)/(2 -x)

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  4. Evaluate: underset(x rarr oo)(lim) (x^((1)/(2)) -2 tan^(-1) ((1)/(x)))...

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  5. Evaluate: underset(x rarr 0)(lim) x^(sin x)

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  6. Prove , using mean value theorem, that |sin alpha -sin beta | le| alph...

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  7. Expand f(x) = (1)/(x) about x =2 upto four terms

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  8. Evaluate underset(theta rarr 0)(lim) (1- cos m theta)/(1- cos n theta)

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  9. Evaluate: underset(xrarr0)lim xlog x

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  10. Determine for which values of x the function y = (x-2)/(x + 1), x ne -...

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  11. Discuss the monotonicity of f(x) = 2x^(3) - 15x^(2) + 36x + 1

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  12. Find the critical number and stationary point f(x) = 2x - 3x^(2)

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  13. Find the absolute extreme for f(x) = 1 - 2x - x^(2) in (-4,1)

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  14. Find the local maximum and local minimum of f(x) = 2x^(3) + 5x^(2) - 4...

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  15. Find the absolute extreme of the function f(x) = 2 cos x in [0, 2pi]

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  16. Find the points of inflection of y = x^(4) - 6x^(2) + 8x -1

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  17. Obtain Maclaurin's series for f(x) = log sec x

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  18. Resistance to motion F of a moving vehicle is given by F = (5)/(x) + 1...

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  19. Find the point on the parabola y^(2) = 2x that is closest to the point...

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  20. Find the asymptotes of the function f(x) = (1)/(x + 1)

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