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1. For a given function (x)
guess an antiderivate (x)
. Show verification that you guess is correct.
(a) (x) = e^(x+1)
.
(b) (x) = e^x+2
(c) (x) = e^(2 x)
(d) (x) = x e^(x^2)
2. Find the most general form of the antiderivative of (x) = 2012
.
3. Find the most general form of the antiderivative of (x) = 2 x+e
.
4. Find the most general form of the antiderivative of (x) = e^(2 x)
.
5. Find the most general form of the antiderivative of (x) = x e^(x^2)
.
6. Find the general form of (x)
if ''(x) = 4 sin x+5 x
. (The general form of http://calculus.sfsu.edu/latexrender?src=%5Cbegin%7Bdisplaymath%7D+%5Ctextstyle%7Bf%7D+%5Cend%7Bdisplaymath%7D&type=png&size=15
has two arbitrary constants.)
7. Find (x)
if '(x) = x
and (2) = 3
.
8. A particle is moving with acceleration ''(t) = t-2
(The derivative is taken with respect to http://calculus.sfsu.edu/latexrender?src=%5Cbegin%7Bdisplaymath%7D+%5Ctextstyle%7Bt%7D+%5Cend%7Bdisplaymath%7D&type=png&size=15
). At time = 0
, (0) = 0
and the velocity '(0) = 5
. Find the position function (t)
at time http://calculus.sfsu.edu/latexrender?src=%5Cbegin%7Bdisplaymath%7D+%5Ctextstyle%7Bt%7D+%5Cend%7Bdisplaymath%7D&type=png&size=15
.
9. Discuss on the forum but do not submit. Show that if ''(x) = G''(x)
, then (x)-G(x)
is a linear function.