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Prove that the tangents to the curve y =...

Prove that the tangents to the curve `y = x^2-7x+12` at (3,0) and (4,0) are at right angles.

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JMD PUBLICATION- A Gift paper from the publishers-Example
  1. Find x, y and z if [[x,+,y,,2],[5,+,z,,xy]]=[[6,2],[5,8]]

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  2. If A= [[cos alpha, -sin alpha],[sin alpha, cos alpha]] , then A + A'= ...

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  3. Prove that the tangents to the curve y = x^2-7x+12 at (3,0) and (4,0) ...

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  4. Integrate int(sin2x)/(a^2sin^2x+b^2cos^2x)dx

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  5. solve int-2^3abs(x-1)dx.

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  6. Find the area of the region bounded by (y^2=4ax) and its latus rectum ...

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  7. Find a unit vector perpendicular to both the vectors (3 hat i + 2 hat ...

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  8. Solve : ((tan^-1 ((2x-3)/(2x-5)) + tan^-1((2x+3)/(2x+5)))=pi/4) .

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  9. Find a for which the function f defined as (f(x)={[(asin(pi/2)(x+1)if...

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  10. If (x=a sin (2t)(1+cos(2t)) and (y=b cos (2t) (1- cos(2t)), then show ...

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  11. int (dx)/(x^2 + 2x + 2) equals :

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  12. Evaluate (int0^(2pi) (1/(1+e^sinx))dx)

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  13. Show that the following differential equation is homogeneous and solve...

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  14. Solve the following differential equation : (((x^2+1)^2 dy/dx +4x(x^2+...

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  15. In a bolt factory, three machines A, B and C manufacturers 25, 35 and...

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  16. Solve by matrix method (3x-4y+2z=-1) (2x+3y+5z=7) (x+z=2)

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  17. If A=[[2,-1],[-1,2]],show that A^2-4A+3I=0.

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  18. Show that the points (0,-1,-1),(-4,4,4),(4,5,1) and (3,9,4) are coplan...

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  19. Find the length of the perpendicular from (2,-3,0) to line ((x+1)/2 = ...

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  20. Maximise (Z=(7x+6y)) subject to ((x+y)le59) , (2xyle80)

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