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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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MODERN PUBLICATION-TEST PAPER 8-EXERCISE
  1. Differentiate : (sec x+ tan x)^cot x.

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  2. If y=e^(ax)sinbx show that y2-2ay1+(a^2+b^2)y=0.

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

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  4. Find the interval in which y=(x-1)^2(x+2) is : (i) increasing (ii)...

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  5. Evaluate : int dx/(x(x^4+1))

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  6. Evaluate : int dx/sqrt (x^2+8x)

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  7. Evaluate : int(0)^(pi/2) e^x cos x dx .

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  8. From the differential equation whose general solution is y=asint+be^t.

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  9. Find the unit vector perpendicular to the plane ABC, where the positio...

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  10. Show that (vec(a)-vec(b))xx(vec(a)+vec(b))=2(vec(a)xxvec(b)).

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  11. The direction cosines of a straight line in two neighbouring positions...

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  12. Find the equation of the plane Passing through the intersection of the...

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  13. Find the equation of the straight line perpendicular to the line (x-2)...

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  14. Exaniming consistency and solvability, solve the following equations b...

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  15. Prove [[a^3-x^3,a^2,a],[b^3-x^3,b^2,b],[c^3-x^3,c^2,c]] = (a-b)(a-c)(b...

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  16. (i) If x=sin t, y=sin 2t then prove that (1-x^2)d^2y/dx^2-xdy/dx+4y=0....

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  17. Show that the radius of the right cicular cylinder of greatest curved ...

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  18. Find the solution of the differential equation x sin (y/x)dy =(y sin...

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  19. Find the area of the region included between the parabola y^(2)=2x and...

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  20. A variable plane is at a constant distance p from the origin and meets...

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