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Prove that f(x)=x^(2)-x sin x is increas...

Prove that `f(x)=x^(2)-x sin x` is increasing on `(0, (pi)/(2))`.

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KUMAR PRAKASHAN-APPLICATION OF DERIVATIVES -PRACTICE WORK
  1. Find the intervals in which f(x)=(4x^(2)+1)/(x) is increasing or decre...

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  2. Find the least value of a such that the function given by f(x)=x^(2)+a...

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  3. Prove that f(x)=x^(2)-x sin x is increasing on (0, (pi)/(2)).

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  4. Find the value of a for which the function f(x)=ax^(3)-3(a+2)x^(2)+9(a...

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  5. Find the in intervals in which f(x)=sin^(4)x+cos^(4)x is increasing or...

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  6. f : (0, pi)to R, f(x)=2x+cot x. Find the intervals in which f(x) is st...

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  7. Show that f(x)=x^(3)-3x^(2)+4x, x in R is strictly increasing on R.

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  8. Without using differentiation, prove that f(x)=ax+b, where a gt 0 is s...

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  9. f : R^(+)to R^(+), f(x)=(log x)/(sqrt(x)). Find the intervals in which...

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  10. Find the equation of the tangent to the curve y^(2)=16x which is paral...

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  11. Find the equation of the normal to the curve y = 8x which is perpendic...

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  12. Prove that the curves x^(2)+y^(2)=ax and x^(2)+y^(2)=by are cuts ortho...

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  13. Find the equation of the tangent and normal to the curve y^(2)(a+x)=x^...

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  14. Show that the normal to the curve 5x^(5)-10x^(3)+x+2y+6=0 at P(0,-3) i...

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  15. Show that a point at which the line (x)/(a)+(y)/(b)=1 touches to the c...

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  16. A line x cos alpha + y sin alpha = P is a tangent to the curve (x^(2))...

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  17. Find the equations of the tangent to the curve y=cos(x+y) which is par...

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  18. Find the points on the curve x^(2)y^(2)+xy=2 at which the slope of the...

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  19. The slope of the tangent to the curve xy+ax+by=2 at a point (1, 1) the...

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  20. Prove that all points on the curve y^(2)=4a[x+a sin((x)/(a))] at which...

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