Homework 3/31
Part 1:
1. Use differentials to approximate (2
.
002)
5
.
2. Use differentials to approximate (1
.
997)
5
.
3. Use differentials to approximate (2 +
h
)
5
.
4. Use differentials to approximate (
x
)
5
near
x
= 2.
NOTE: Your answer to this problem is called the
linearization of
x
5
at
x
= 2.
5. Graph
y
=
x
5
and the linearization at
x
= 2 on the same axes. Your graph must extend at
least from
x
= 0 to
x
= 3.
6. Use your linearization to solve
x
5
= 35.
7. Use your calculator to solve
x
5
= 35.
Part 2:
Warning!. Work this problem in radians!
1. Use differentials to approximate tan 46
◦
.
[Hint: Convert Δ
x
= 1
◦
to radians.]
2. Use differentials to approximate tan 44
◦
.
3. Use differentials to approximate tan(
π/
4 +
h
).
4. Use differentials to approximate tan
x
near
x
=
π/
4. Simplify your answer.
NOTE: Your answer to this problem is called the
linearization of
tan
x
at
x
=
π/
4.
5. Graph
y
= tan
x
and your answer to part (4) on the same axes. Your graph must extend at
least from
x
= 0 to
x
=
π/
2.
6. Use your linearization to solve tan
x
= 5
/
6.
7. Use your calculator to solve tan
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 Spring '08
 STAFF
 Calculus, approximate tan

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