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If f' (x) =xe^(x) and f(0)=1, find f(x)...

If f' (x) `=xe^(x)` and f(0)=1, find f(x)

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The correct Answer is:
`f(x)=e^(x)(x-1)+2`
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CHHAYA PUBLICATION-DIFFERENTIAL EQUATIONS OF THE FIRST ORDER AND FIRST DEGREE -PART -E
  1. If f' (x) =xe^(x) and f(0)=1, find f(x)

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  2. If f'(x)=logx and f(1)=0, show f(x)=x(logx-1)+1.

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  3. A curve passes through the point (3,-4) and the slope of the tangent t...

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  4. Determine the equation of the passing through the origin, the slope of...

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  5. The slope of the tangent to a curve at any point (x,y) is (3y+2x+4)/(4...

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  6. Show that, the family of curves for which the slope of the tangent at ...

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  7. A curve is passing through the point (4,3) and at any point the gradie...

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  8. Show that, the equation of the curve passing through (1,0) and satisfy...

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  9. A curve passes through tha point (2,0) and satisfies the equation ydy+...

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  10. A motor boat is moving in a straight line. Its velocity is V when the ...

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  11. A particle starts from the origin and moves along a straight line. If ...

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  12. The velocity of a particle moving in a straight path is given by v=16t...

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  13. The acceleration of a particle moving along a straight line is (6t^(2)...

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  14. If the acceleration of a particle at time t seconds be 1.2t^(2)ft//s^(...

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  15. A particle starts form the origin with a velocity of 10 cm/s and moves...

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  16. A particle starts from the origin with a velocity of 2 cm/s and moves ...

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  17. In a certain culture, the number of bacteria at any instant increases ...

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  18. A radioactive substance is subject to the law of natural decay (dv)/(d...

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  19. Suppose the marginal cost of a product is given by RS(10+24x-3x^(2)), ...

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  20. If the marginal revenue function is (15-2x-x^(2)), find total revenue ...

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