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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)(sinx+cosx),` `x" ">" "0` is always an strictly increasing function in `(0,pi/4)` .

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XII BOARDS PREVIOUS YEAR-XII Boards-All Questions
  1. For what value of k is the function f(x) = { k|x|/x, x<0; 3, x>=0 con...

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  2. Use product [1-1 2 0 2-3 3-2 4][-2 0 1 9 2-3 6 1-2] to solve the sy...

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  3. Show that the function f given by f(x)=tan^(-1)(sinx+cosx), x" ">" "0 ...

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  4. Find the matrix X so that X[[1, 2, 3],[ 4 ,5, 6]]= [[-7,-8,-9],[2,4,6]...

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  5. If y=e^"tan"^((-1)"x"), prove that (1+x^2)y2+(2x-1)y1=0.

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  6. Find int2x sin (3x + 1) dx

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  7. Find the image of the point having position vector hat i+3 hat j+4 ha...

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  8. Given A=((2,-3),(-4,7)) compute A^(-1) and show that 2A^(-1)=9I-A

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  9. Differentiate tan^(-1)((1+cosx)/sinx) with respect to x

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  10. Find the value of tan^(-1) sqrt3 - cot^(-1) (-sqrt3)

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  11. The total cost C(x) in Rupees, associated with the production of x ...

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  12. Integrate the functions (cos2x+2sin^2x)/(cos^2x)

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  13. Find the differential equation representing the family of curves y=ae^...

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  14. If the matrix A = [[0,a,-3],[2,0,-1],[b,1,0]] is skew symmetric, find ...

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  15. If theta is the angle between two vectors hati-2hatj+3hatk and 3hati-2...

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  16. Find the magnitude of each of the two vectors veca and vec b having th...

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  17. A black and a red dice are rolled. (a)   Find the conditional proba...

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  18. Using properties of determinants prove that |(1,1, 1+3x),(1+3y,1,1),(1...

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  19. Find (dy)/dx, if (x^2+y^2)^2=xy

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  20. If a * b, denoted the larger of 'a' and 'b' and if a o b = a*b + 3 , ...

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