In the following exercises, verify that the given choice of n in the remainder estimate | R n | ≤ M ( n + 1 ) ! ( x − a ) n + 1 where M is the maximum value of | f ( n + 1 ) ( z ) | on the interval between a and the indicated point, yields | R n | ≤ 1 1000 . Find the value of the Taylor polynomial P n of f at the indicated point. 131. Integrate the approximation e x ≈ 1 + x + x 2 2 + ... + x 6 720 evaluated at −x 2 to approximate ∫ 0 1 e − x 2 d x .
In the following exercises, verify that the given choice of n in the remainder estimate | R n | ≤ M ( n + 1 ) ! ( x − a ) n + 1 where M is the maximum value of | f ( n + 1 ) ( z ) | on the interval between a and the indicated point, yields | R n | ≤ 1 1000 . Find the value of the Taylor polynomial P n of f at the indicated point. 131. Integrate the approximation e x ≈ 1 + x + x 2 2 + ... + x 6 720 evaluated at −x 2 to approximate ∫ 0 1 e − x 2 d x .
In the following exercises, verify that the given choice of n in the remainder estimate
|
R
n
|
≤
M
(
n
+
1
)
!
(
x
−
a
)
n
+
1
where M is the maximum value of
|
f
(
n
+
1
)
(
z
)
|
on the interval between a and the indicated point, yields
|
R
n
|
≤
1
1000
. Find the value of the Taylor polynomial Pnof f at the indicated point.
131. Integrate the approximation
e
x
≈
1
+
x
+
x
2
2
+
...
+
x
6
720
evaluated at −x2to approximate
∫
0
1
e
−
x
2
d
x
.
Perform the bisection method to provide a root for f (x) = x² + 3x – 2 given ɛ = 0.001. The first
three (3) steps were already done in class.
Let x1 = 0, x2 = 1, and x3 = 0.5. Then (0.5) = –0.25 .
Redefine x1 = 0.5, x3 = 0.75. Then f (0.75) = 0.8125.
Redefine x2 =
0.75, хз
= 0.625. Then f(0.625) = 0.2656.
= 0.5625. Then f (0.5625) = 0.0039.
Redefine x2 =
0.625, x3
Redefine
,X3 =
Then f (x3) =
Redefine
X3 =
Then f (x3)
Redefine
X3 =
Then f (x3) =
Redefine
X3 =
Then f (x3) =
Redefine
X3 =
Then f (x3) =
Redefine
, X3 =
Then f (x3) =
Since |f (x3)| <
take x =
Let f(x) = 1.26x* – x + 1.85x² + 1.32x – 3. Determine the approximate root with at most 15% error
estimate on the interval [-2,-1). (Using Bisection Method)
B. -1.375
A. -1.875
C. -1.125
D. -1.625
Find the maximum error if the approximation 1 + x + x2/2 is used to approximate ex on the interval [0,2] - using Taylor's inequality.
Mathematics for Elementary Teachers with Activities (5th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.