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

If `y=e^(ax)sinbx` show that `y_2-2ay_1+(a^2+b^2)y=0`.

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MBD PUBLICATION-THREE DIMENSIONAL GEOMETRY-QUESTION BANK
  1. Find the derivative of tan^-1 (sqrt(1-x^2)/x)with respect to cos^-1x .

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  2. Find (d^2y)/(dx^2) if x=a costheta,y=bsintheta.

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

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  4. If x^7y^3=(x+y)^10, then find (d^2y)/(dx^2)

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  5. If u=f((x^2+y^2)/xy) prove that x(partialu)/(partialv)+y(partialu)/(pa...

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  6. If f(x+y)=f(x).f(y) forall x,y and f(5)=2 and f'(0)=3, then show that ...

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  7. If (fog) (1)=3, g(1) = 2, g(1) = 1,then show that f(2)=3.

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  8. If f(a)= 2, f'(a) = 1, g(a)=-1 and g'(a)=2, then find underset(xtoa)li...

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  9. Find the rate of change of the area of circle w.r.t.r when r=8 cm.

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  10. The side of a sqart is increasing at the rate of 0.1 cm//sec and at th...

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  11. A particle moves along a straight line according to the law s=t^3-3t^...

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  12. Show that the function f(x)=1/x is decreasing in (0,oo).

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  13. Find the intervals where the function f(x)=x^3-12x+10 is increasing.

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  14. Find the slope of the normal to the curve y=xe^-x at x=2.

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  15. Find the angle between the tangents to the curve y=x^2-5x+6 at the poi...

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  16. Find the point on the curve y^2 - x^2 + 2x - 1 =0 where the tangent ...

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  17. Find the points on the curve 9y^2=x^2, where normal to the curve makes...

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  18. If y=x^4-12 and if x changes from 2 to 1.99, find the approximate erro...

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  19. Using differential find the value of sqrt(16.2).

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  20. Show that f(x)=x^3-6x^2+24x+4 has neither a maximum nor a minimum valu...

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