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Use the function f(x) = x^(1//x), x gt 0...

Use the function `f(x) = x^(1//x), x gt 0` to show that `e^(pi) gt pi^(e)`.

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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
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  2. Show that the line y = mx + c touches the parabola y^(2) = 4ax if c = ...

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  3. Use the function f(x) = x^(1//x), x gt 0 to show that e^(pi) gt pi^(e)...

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  4. Let f(x)={(absx/x,if xne0),(0,if x=0):} Examine the continuity of f(x)...

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  6. Determine the area within the ellipse x^2/a^2+y^2/b^2=1.

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  7. int0^pi(xsinxdx)/(1+cos^2x)

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  8. Evaluate the following integrals int(3sinx+28cosx)/(5sinx+6cosx)dx

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  14. Prove that intdx/((x-1)^2(x+2))=1/9ln abs((x+2)/(x-1))-1/(3(x-1))+c

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  15. int0^pi((xtanx)/(secx+tanx))dx

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