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Find the slope of the normal to the curv...

Find the slope of the normal to the curve `y=xe^-x` at x=2.

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`y=xe^-xrArr(dy)/dx=x(-e^-x)+e^-x=e^-x(1-x)` Slope of the tangent at x=2
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MBD PUBLICATION-THREE DIMENSIONAL GEOMETRY-QUESTION BANK
  1. Show that the function f(x)=1/x is decreasing in (0,oo).

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  2. Find the intervals where the function f(x)=x^3-12x+10 is increasing.

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  3. Find the slope of the normal to the curve y=xe^-x at x=2.

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  4. Find the angle between the tangents to the curve y=x^2-5x+6 at the poi...

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  5. Find the point on the curve y^2 - x^2 + 2x - 1 =0 where the tangent ...

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  6. Find the points on the curve 9y^2=x^2, where normal to the curve makes...

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  7. If y=x^4-12 and if x changes from 2 to 1.99, find the approximate erro...

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  8. Using differential find the value of sqrt(16.2).

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  9. Show that f(x)=x^3-6x^2+24x+4 has neither a maximum nor a minimum valu...

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  10. Find the points where f(x)=8x^2-x^4-4 has local maximum or minimum.

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  11. Find the absolute maximum and absolute minimum value of the function f...

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  12. Find the absolute maximum and absolute minimum value of f(x)=x-x^3 in ...

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  13. Using mean value theorem, prove that sin xltx,in(0.pi//2).

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  14. Write antiderivative of tan^2x

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  15. Write the vale of intxa^(x^(2+1))dx

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  16. Write the vale of intsqrt(1-cos2x)dx

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  17. If f'(x)= e^x+1/(1+x^2),what is f(x) ?

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  18. Write the value of inte^(logcot^2x)dx

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  19. Write the value of int(e^x-1)/(1-e^(-x))dx

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  20. Write the value of int(e^x-1)/(1-e^-x)dx

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