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Use the function f(x) = x^(1/x),x gt 0 t...

Use the function f(x) = `x^(1/x),x gt 0` to show that e^pi )grt pi^e.

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SHARAM PUBLICATION-MODEL QUESTION PAPER-3-EXERCISE
  1. If f(x) = a In x + bx^2 + x has extreme values at x= - 1 and x = 2 the...

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  2. Evaluate the following integrals : int(cos^(-1)x)/(sqrt(1-x^(2)))dx.

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  3. Evaluate int(sin x - cos x)dx.

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  4. Prove that int0^(pi/2)lnsinxdx=pi/2ln( 1 /2)

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  5. Determine the area the of the region between the curves y=cos x and y=...

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  6. Solve the differential equation (1+x^2)(dy)/(dx)+y= tan^(-1)x

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  7. Show by vector method that the line joining the points (1, 4, 2) and ...

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  8. Find the co-ordinates of the point where the perpendicular from the or...

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  9. Find the equation of the plane passing through the line x = y = z and ...

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  10. Find the co-ordinates of the point where the (x - 2)/3 = (y+1)/4=(z-2)...

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  11. Show that the relation S defined on set N xx N by (a, b) S(c,d) rArr a...

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  12. Solve for x, "tan"^(-1)((2x)/(1-x^(2)))+""cot"^(-1)((1-x^(2))/(2x))=...

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  13. Find graphically the maximum value of z = 2x + 5y subject to the const...

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  14. Find the values of a and b such that the function f defined by f(x) = ...

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  15. Use the function f(x) = x^(1/x),x gt 0 to show that e^pi )grt pi^e.

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  16. Evaluate int((1+sinx)/(1+cosx))e^(x)dx.

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  17. Evaluate int0^ pi x/(1+ sin x) dx

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  18. Find the solution of the following differential equations: (2x+y+1)dx+...

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  19. If veca,vecb and vecc are three vectors such that |veca|= 3,|vecb|= 4 ...

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  20. Find the coordinates of foot of perpendicular drawn from the point (0,...

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