Calculus test questions

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September 7th 2010, 01:49 AM
johnsy123

Calculus test questions

1) The curve with equation y=f(x) passes through the point (3,-1) and f '(x)=2x+5. find f(x).

2) find s in terms of t, if ds/dt=t+3-1/t^2 and s=6 and t=1.
September 7th 2010, 01:53 AM
Prove It

1) $f'(x) = 2x + 5$

$f(x) = \int{2x + 5\,dx}$

$f(x) = x^2 + 5x + C$ .

You know that the point $(3, -1)$ lies on the curve, so substitute it in and solve for $C$ .

2) $\frac{ds}{dt} = t + 3 - \frac{1}{t^2}$

$\frac{ds}{dt} = t + 3 - t^{-2}$

$s = \int{t + 3 - t^{-2}\,dt}$

$s = \frac{t^2}{2} + 3t - \frac{t^{-1}}{-1} + C$

$s = \frac{t^2}{2} + 3t + \frac{1}{t} + C$ .

Now substitute $s = 6$ and $t = 1$ to find $C$ .

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