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If ye^y=x prove that (dy)/(dx)= y/(x(1+y...

If `ye^y=x` prove that `(dy)/(dx)= y/(x(1+y))`

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If e^y(x+1)=1 , prove that (d^2y)/(dx^2)=((dy)/(dx))^2

If y^(x)=e^(y-x)" prove that, " (dy)/(dx)=((logey)^(2))/(log y) .

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If y=x^(y^(x)) , prove that, (dy)/(dx)=(y log y(1+x logx log y))/(x logx(1-x logy)) .

If y log x= x-y , prove that (dy)/(dx)= (log x)/((1+log x)^(2))

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UNITED BOOK HOUSE-SET 8-EXERCISE
  1. Evaluate : sec^2(tan^(-1)2)+cosec^2(cot^(-1)3).

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  2. Prove that , |[1,logx^y,logx^z],[logy^x,1,logy^z],[logz^x,logz^y,1]|=0

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  3. If A = [[2,2],[4,3]] show that AA^(-1)=I2where I2 is the unit matrix o...

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  4. f(x) = { (kx+1, x le pi),( cos x, x >pi):} If f(x) is continous at x =...

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  5. If ye^y=x prove that (dy)/(dx)= y/(x(1+y))

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  6. Evaluate: int e^x/x(x log x+1)dx

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  7. Find the integrating factor of the differential equation xlogx (dy)/(d...

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  8. Find the acute angle between the pair of straight lines whose directio...

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  9. Find the equation of the plane which passes through the points (1,2,3)...

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  10. A random variable X has the following probability distribution: ...

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  11. If cos^(-1)x+cos^(-1)y= theta, show that x^2-2xycos theta+y^2 = sin^2 ...

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  12. If A = [[cos alpha,sin alpha],[-sin alpha,cos alpha]] then prove that,...

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  13. If tan y = (tan x+sec x-1)/(tanx -sec x+1) show that (dy)/(dx) = 1/2

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  14. Evaluate: int (dx)/(1-cos alpha cos x)(0< alpha < pi/2)

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  15. Evaluate: int ((sinx+cos x)dx)/(sin(x-a))

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  16. The vectors vec a and vec b are non collinear. If vec p = (x+4y)veca+ ...

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  17. evaluate overset(1)underset(-1)int (2x+3)/(4)dx

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  18. Show that the standard deviation of a binomial distribution (with para...

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  19. Prove that, a conical tent of given capacity will required the least a...

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  20. Show that the normal at any point theta to the curve x=acostheta+at...

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