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If y={"log"(x+sqrt(x^2+1))}^2,"s h o wt...

If `y={"log"(x+sqrt(x^2+1))}^2,"s h o wt h a t"(1+x^2)(d^2y)/(dx^2)+x(dy)/(dx)=2.`

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If y={log(x+sqrt(x^(2)+1))}^(2), show that (1+x^(2))(d^(2)y)/(dx^(2))+x(dy)/(dx)=2

If y={log(x+sqrt(x^(2)+1))}^(2), show that (1+x^(2))(d^(2)y)/(dx^(2))+x(dy)/(dx)=2

If y=log(x+sqrt(1+x^(2))), then show that (1+x^(2))(d^(2)y)/(dx^(2))+x(dy)/(dx)=0

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If y=log[x+sqrt(x^(2)+1)], prove that (x^(2)+1)(d^(2)y)/(dx^(2))+x(dy)/(dx)=0

If y=log[x+sqrt(x^(2)+a^(2))], show that ((x^(2)+a^(2))(d^(2)y)/(dx^(2))+x(dy)/(dx)=0

If y=(x+sqrt(1+x^(2)))^(n) then (1+x^(2))(d^(2)y)/(dx^(2))+x(dy)/(dx)

(i) If y^(1//m) + y^(-1//m) = 2x then prove that (x^(2)-1) (d^(2)y)/(dx^(2)) + x (dy)/(dx) - m^(2)y =0 (ii) If y = ln (x + sqrt(1+x^(2)) , then prove that (1+x^(2)) (d^(2)y)/(dx^(2)) + x (dy)/(dx)=0

If y=log{x+sqrt(x^(2)+a^(2))}, prove that: (x^(2)+a^(2))(d^(2)y)/(dx^(2))+x(dy)/(dx)=0

MODERN PUBLICATION-PROBABILITY-MOCK TEST (Answer the following questions)
  1. Find intxcosxdx

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  2. Find: int(x^(3))/(sqrt(1-x^(8)))dx.

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  3. int1/(sqrt(5-4x-2x^2))dx

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  4. Find the integrating factor of xlogx(dy)/(dx)+y=2-logx.

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  5. If tan^(-1)((x-2)/(x-4))+tan^(-1)((x+2)/(x+4))=(pi)/(4), find the valu...

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  6. Let T be the set of all triangles in a plane with R a relation in T g...

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  7. Find (dy)/(dx), when: (cosx)^(y)=(cosy)^(x)

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  8. Find the equation of the tangent to the curve x^(2) + 3y = 3, which is...

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  9. Prove that: [vec(a)" "vec(b)" "vec( c )+vec(d)]=[vec(a)" "vec(b)" "vec...

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  10. Find the values of lamda and mu for which (2hat+6hatj+27hatk)xx(hati+l...

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  11. Find the points on the line (x+2)/3=(y+1)/2=(z-3)/2\ at a distance...

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  12. If A and B are two independent events, then the probability of occu...

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  13. Let f: W to W be defined by: f(n)={{:(n-1",","if n is odd"),(n+1",","i...

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  14. Differentiate sin^(-1)((2^(x+1))/(1+4^(x))) w.r.t. x.

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  15. If y={"log"(x+sqrt(x^2+1))}^2,"s h o wt h a t"(1+x^2)(d^2y)/(dx^2)+x(...

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  16. Find the general solution of the differential equation: cos^(2)x(dy)/(...

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  17. Evaluate the definite integrals int0pi/2(cos^2x dx)/(cos^2x+4sin^2x...

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  18. Bag I contains 3 red and 4 black balls and Bag II contains 4 red an...

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  19. three numbers are selected at random (without replacement) from first ...

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  20. A factory manufactures two types of screws, A and B. Each type of scre...

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