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Find the interval on which the function ...

Find the interval on which the function f(x)=`x^x` decreases.

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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. If x^2+y^2=t-1/t and x^4+y^4=t^2+1/t^2 then prove that x^3ydy/dx=1.

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  2. Find the maximum and minimum of f(x)=|x+3|,for all x belongs to R.

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  3. Find the interval on which the function f(x)=x^x decreases.

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  4. Find the solution of the following differential equations: (4x+6y+5)dx...

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  5. Integrate int((1-cosx)/(1+cosx))dx .

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  6. Solve (x+y)^(2)(dy)/(dx)= a^(2).

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  7. If f is periodic with period 3 and f(1) = 1 then what is the value of ...

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  8. Evaluate int(-2)^2abs([x])dx .

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  9. Prove that (vec a × vec b)^(2) = a^(2)b^(2)-(vec a . vec b)^(2).

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  10. Find the perpendicular distance of the point (-1,3,9) from the line (x...

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  11. Prove that (vecaxxhati)^2+(vecaxxhatj)^2+(vecaxxhatk)^2=2veca^2 .

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  12. Find the equation of planes passing throught the points (6,-1,1), (5,1...

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  13. Find the co-ordinates of the foot of the perpendicular drawn from the ...

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  14. If e^(y//x)=(x)/(a+bx) then show that x^(3)(d)/(dx)((dy)/(dx))=(x(dy)/...

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  15. If 2x=y^(1/m)+y^(-1/m) , then prove that (x^2-1)y(n+2)+(2n+1)xy(n+1)+(...

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  16. Show that the rectangle of maximum area that can be inscribed in a giv...

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  17. Prove the following by vector method. Altitudes of a triangle are conc...

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  18. Find the magnitude and equation of the line of shotest distance betwee...

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  19. Solve the following by matrix method x-y+z=4, 2x+y-3z=0, x+y+z=2

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  20. Prove that abs((-2a,a+b,c+a),(a+b,-2b,b+c),(c+a,c+b,-2c))=4(b+c)(c+a)(...

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