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Find f''(x) in each of the following cas...

Find f''(x) in each of the following cases:
`f(x)=1/(x^2-5x+6)`

Text Solution

Verified by Experts

The correct Answer is:
`2[1/(x-3)^3-1/(x-2)^3]`
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Use the Factor Theorem to determine whether g (x) is factor of f(x) in each of the following cases: (i) f (x) = 5x ^(3) + x ^(2)-5x -1, g (x)=x +1 (ii) f (x) = x ^(3) + 3x ^(2) + 3x +1 , g(x) =x +1 (iii) f (x) =x ^(3) - 4x ^(2) +x + 6, g (x) =x -2 (iv) f (x) = 3x ^(3) - 20x + 12, g (x) = 3x -2 (v) f (x) = 4x ^(3) + 20 x ^(2) + 33 x +18, g (x) =2x +3

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CHHAYA PUBLICATION-SECOND ORDER DERIVATIVE-Short Answer type Question
  1. Find f''(x) in each of the following cases: f(x)=1/(x^2-5x+6)

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  2. Find f''(x) in each of the following cases: f(x)=1/(x^2-4)

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  3. Find f''(x) in each of the following cases: f(x)=sinx sin2x sin 3x

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  4. Find f''(x) in each of the following cases: f(x)=e^xsin^2x

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  5. Find f''(x) in each of the following cases: f(x)=xsqrt(a^2-x^2)

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  6. Find (d^2y)/(dx^2) when: tany=(sqrt(1+x^2)-1)/x

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  7. Find (d^2y)/(dx^2) when: y=tan(x+y)

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  8. Find (d^2y)/(dx^2) when: sinx+cosy=1

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  9. Find (d^2y)/(dx^2) when: x^py^q=(x+y)^(p+q)

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  10. Findy2 in each of the following cases: x=acos^3theta,y=asin^3theta

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  11. Findy2 in each of the following cases: x=a(theta+sintheta),y=a(1-cost...

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  12. Findy2 in each of the following cases: x=a(t+1/t),y=a(t-1/t)

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  13. Findy2 in each of the following cases: x=e^t,y=sint at t=pi/2

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  14. Findy2 in each of the following cases: x=a(costheta+thetasintheta),y=...

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  15. Findy2 in each of the following cases: sinx=(2tantheta)/(1+tan^2theta...

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  16. Find y2 in each of the following cases: y=t^2+t^3,x=t-t^4

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  17. IF y^3=x^2+y^2, find (d^2y)/(dx^2) at y=1.

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  18. IF y=x/(x^2-x-2), find the value of y2 at x=1.

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  19. IF y=xsinx, prove that, x^2(d^2y)/(dx^2)-2xdy/dx+(2+x^2)y=0

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  20. If y=ae^(mx)+bcosmx, prove that, (d^2y)/(dx^2)+m^2y=2am^2e^(mx)

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