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Prove the inequality x^2e^(-x^2) le e^...

Prove the inequality
`x^2e^(-x^2) le e^(-1),x in R`.

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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Solve : [[7,6,x],[2,x,2],[x,3,7]] = 0

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  2. Verify that [AB]^T = B^T A^T whereA=[[1,2,3],[3,-2,1]],B=[[1,2],[2,0],...

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  3. Prove the inequality x^2e^(-x^2) le e^(-1),x in R.

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  4. Prove that d/dxlntan(pi/4+x/2)=secx.

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  5. Determine the point on the curve y = ln x, at which the tangent will b...

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  6. Find the angle of intersection of two curves y =2^x and y=5^x

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  7. If 2y=x(1+(dy)/(dx)), then show that y(2) is a constant.

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

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  9. int(xe^x)/(1+x^2)dx

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  10. Solve dy/dx-y=e^x.

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

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  12. intdx/(sqrtx-root(3)(x))(x=t^6)

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

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  14. Show that [veca+vecbvecb+veccvecc+veca] = 2[vecavecbvecc]

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  15. Find the points of intersection of the line (x-1)/1=(y+2)/ 3 =(z-1)/(...

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  16. If the magnitude of the difference of two unit vectors is sqrt3 then f...

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  17. Using vector method prove that cosA=(b^2+c^2-a^2)/(2bc)

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  18. If 2s=a+b+c show that [[a^2,(s-a)^2,(s-a)^2],[(s-b)^2,b^2,(s-b)^2],[...

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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. In any triangle ABC, prove by vector method that frac[a][sinA]=frac[b]...

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