Worksheet ----MS125 Calculus I Dr. Y. Kim
4.1 Linear Approximation
The Linear Approximation
Suppose
)(xf is differentiable at
a
x
=
. Then
•
the Linear Approximation is
xaff
∆
′
≈
∆
)(
•
the linearization of )(xf at
a
x
=
is ))(()()(
axafafxf
−
′
+
≈
for values of
x
near
a
.
•
the error, )(
xE
, in the approximation is defined by
))(()()(
)()(
axafafxf
xaffxE
−
′
−−=
∆
′
−∆=
Ex1) The position of an object in linear motion at time t (sec) is mttts 320)(
3
+−= . Estimate the
distance traveled over the time interval ]025.3,3[ .
Ex2) What is the tangent line approximation(linearization) for xxf sin)(
=
near 0
=
x?
Ex3) Let
x
exf
3
)( =. What is the linearization of )( xf at 0
=
x?
Ex4) Use the Linear Approximation to estimate 2324 −. Find the error using a calculator.
HOMEWORK :1~7 odd, 16, 17, 18, 25, 26