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Show that f(x)=tan^(-1)(sinx+cosx) is an...

Show that `f(x)=tan^(-1)(sinx+cosx)` is an increasing function on the interval `(0,\ pi//4)` .

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CBSE COMPLEMENTARY MATERIAL-APPLICATION OF DERIVATIVES-4 MARK QUESTIONS
  1. Find the intevals in which the following functionis decreasing. f(x) =...

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  2. Find the interval in which the function f(x)=5x^((3)/(2))-3x^((5)/(2))...

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  3. Show that f(x)=tan^(-1)(sinx+cosx) is an increasing function on the ...

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  4. Find the interval in which the function f(x) =cos^(-1) ((1-x^(2))/(1+x...

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  5. Find intervals in which the function given by f(x)=3/(10)x^4-4/5x^3-3x...

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  6. Find the equation of the tangent to the curve (x^(2))/(a^(2))-(y^(2))/...

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  7. Find the equation of the tangent line to the curve y=x^2-2x+7which is(...

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  8. Find the required point be P(x1, y1)dot The tangent to the curve sqrt(...

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  9. Find a point on the parabola y=(x-3)^2 , where the tangent is pa...

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  10. Find the equation of the normal to the curve y=e^(2x)+x^(2)" at "x=0. ...

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  11. The line (x)/(a)+(y)/(b)=1 touches the curve y=be^(-x//a) at the point

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  12. At what point on the circle x^(2)+y^(2)-2x-4y+1=0 the tangent is paral...

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  13. Show that the equation of the normal at any point 'theta' on the curve...

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  14. Show that the curves x y=a^2a n dx^2+y^2=2a^2 touch each other

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  15. For the curve y=5x-2x^3 , if x increases at the rate of 2 units/sec, t...

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  16. Find the condition for the curve (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 and...

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  17. Show that the curves y=a^(x) and y=b^(x), a gt b gt 0 intersect at an ...

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  18. Find the equation of the normal to the curve ay^(2)=x^(3) at the point...

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  19. Find the equation of the normal at a point on the curve x^(2)=4y, whic...

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  20. Find the point on the curve 9y^2=x^3, where the normal to the curve ma...

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