Math 119 Recitation 12
December 5, 2006
1. Differentiate
(a)
y
= arcsin
√
1

x
2
(b)
y
= arctan
1

x
1+
x
(c)
y
= arctan (sin
x
)
(d)
y
= tanh (ln
x
)
2. Find the tangent line to the curve arctan (
2
x
y
)

πx
y
2
= 0 at the point (1
,
2).
3. Evaluate the integrals
(a)
2

1
dx
x
2
+2
(b)
dx
x
√
x
2

49
(c)
sinh(2

3
x
)
dx
4. Evaluate the limits
(a) lim
x
→
0
arctan
x
x
(with and without L’Hospital’s rule)
(b) lim
x
→
0
arcsin
x

x
x
3
(c) lim
x
→
π
4
√
2 cos
x

1
1

tan
2
(
x
)
(d) lim
x
→∞
(
x
+1
x

1
)
x
(e) lim
x
→
1
+
(
1
x

1
)
ln
x
(f) lim
x
→∞
(1

4
x
)
x

1
5. A bacteria culture grows with constant relative growth rate. After 2 hours
there are 600 bacteria and after 8 hours the count is 75,000.
(a) Find the initial population.
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 Spring '10
 Tor
 Math, Trigonometry, Inverse function, Inverse trigonometric functions, Elementary special functions, cos x1 limx

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