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MTH143 Midterm Exam 1 Solutions
October 29, 2006
1. (a) One solution is two divide the numerator and denominator by the highest power n2 .
3+5n2
3
0+5
3 + 5n2
2 + 5
n2
=
lim
=5
= lim n+n2 = lim n
n n + n2
n
n 1 + 1
0+1
n
n2
Another solution is to extend t
1. (10 points)
FINAL PART II
(a) Compute the arclength along the curve y =
x2
2
ln(x)
4
between x = 2 and x = 4.
1
dy
=x
dx
4x
Then,
1+
dy
dx
2
2
1
=1+ x
4x
1
1
= 1 + x2 +
2 16x2
1
1
= x2 + +
2 16x2
2
1
= x+
4x
Therefore, the arclength integral is
L=
4
2