MTH 151
Quiz 6
Fall 2011
Show all work in a neat and organized fashion.
Clearly indicate your answers.
20 points possible.
1. (5 pts.) Use Newton's method to find the root of the given equation
to the best accuracy your calculator will display.
Use the specified initial approximation x1, and show your values for
x2, x3, x4, and so on, until the algorithm stabilizes.
x3−x2−1=0, x1=1
Recall that
x2=x1−
f(x1)
f′(x1)
and xn+1=xn−
f(xn)
f′(xn)
.
2. (5 pts.) Find the most general antiderivative of f(x)=x−5+sec2 x.
In other words, find the indefinite integral.
⌠ ⌡
(x−5+sec2 x) dx
3. (5 pts.) Find f(x), given the following.
f′(x)=√x· (30+60x), f(1)=50
4. (5 pts.) A particle is moving with the given data. Find the position
function of the particle.