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Show that the function f given by f(x)=t...

Show that the function f given by `f(x)=tan^(-1)(sin x + cos x), x gt 0` is always an increasing function in `(0, (pi)/(4))`.

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KUMAR PRAKASHAN-APPLICATION OF DERIVATIVES -TEXTBOOK ILLUSTRATIONS FOR PRACTICE WORK
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  2. Find all the points of local maxima and local minima of the function f...

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  3. Find two positive numbers whose sum is 15 and the sum of whose squares...

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  4. Find the shortest distance of the point (0, c) from the parabola y=x^(...

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  5. Let AP and BQ be two vertical poles at points A and B respectively. If...

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  7. Prove that the radius of the right circular cylinder of greatest curve...

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  8. Find the global maximum and minimum values of the function f given by ...

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  9. Find absolute maximum and minimum values of a function f given by f(x...

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  10. An Apache helicopter of enemy is flying along the curve given by y=x^(...

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  11. A car starts from a point P at time t = 0 seconds and stops at point Q...

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  12. A water tank has the shape of an inverted right circular cone with its...

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  13. A man of height 2 metres walks at a uniform speed of 5 km/h away from ...

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  14. Find the equation of the normal to the curve x^(2)=4y which passes thr...

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

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  16. Find intervals in which the function given by f(x)=(3)/(10)x^(4)-(4)/(...

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  17. Show that the function f given by f(x)=tan^(-1)(sin x + cos x), x gt 0...

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  18. A circular disc of radius 3 cm is being heated. Due to expansion, its ...

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  19. An open topped box is to be constructed by removing equal squares from...

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  20. Manufacturer can sell x items at a price of rupees (5-(x)/(100)) each....

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