Question

f(x)=ln(1+2x), a=4,n=3,3.7<=x<=4.3

(b) Use Taylor's Inequality to estimate the accuracy of the
approximation *f* *T _{n}(x)* when

Answer #1

Given that

The accuracy of the approximation is estimated by the Taylor's inequality

The (n+1)th i.e. 4th derivative of the function f(x) is

Now,

Rounding the answer to four decimal places, we get that the accuracy of the approximation is 0.

Consider the following function.
f(x) = ln(1 + 2x), a =
1, n = 3, 0.8 ≤ x ≤
1.2
(a) Approximate f by a Taylor polynomial with degree
n at the number a.
T3(x) =
(b) Use Taylor's Inequality to estimate the accuracy of the
approximation
f(x) ≈ Tn(x) when x lies in the given
interval. (Round your answer to six decimal places.)
|R3(x)| ≤
(c) Check your result in part (b) by graphing
|Rn(x)|.

A) Use the Linear Approximation to estimate Δf
= f(4.9) − f(5) for
f(x) = x −
6x2.
Δf ≈
B)Estimate the actual change.
Δf =
C)Compute the error in the Linear Approximation
D)Compute the percentage error in the Linear Approximation.
(Round your answer to five decimal places.)

Consider the following.
f(x)=ln(1-x)
a) Determine the fourth Taylor polynomial of
f(x) at x = 0.
b) Use the above to estimate ln(0.6). (Give your answer correct the
four decimal places.)

1) Use finite approximation to estimate the area under the graph
of f(x) = x^2 and above the graph of f(x) = 0 from Xo = 0 to Xn= 2
using
i) a lower sum with two rectangles of equal width
ii) a lower sum with four rectangles of equal width
iii) an upper sum with two rectangles of equal width
iv) an upper sum with four rectangles if equal width
2) Use finite approximation to estimate the area under...

f(x)=1/2x ln x^4, (-1,0)
a) find an equation of the tangent line to the graph of the
function at the indicated point.
b) Use a graphing utility to graph the function and its tangent
line at the point.

Estimate the area under the graph of f(x)=1/(x+3) over the
interval [−2,1] using ten approximating rectangles and
right endpoints. a=-2,b=1,n=10
Rn=?
Repeat the approximation using left endpoints.
Ln?
Accurate to 4 places.

A. The derivative of f(x)=(5x3+4)(6ln(x)-2x)
B. The derivative of c(x)=ln(4x3-x2)

find absolute max and min
f(x)= ln(x^3 -2x^2 +x) [1/4, 3/4]

Find derivatives (Please show work!)
1. f(x)=ln(5x^3)
2. f(x)=(ln^3)x
3. f(x)=e^(5x2+2)
4. f(x)=xe^2x
5. f(x)=xlnx

2. Let f(x) = sin(2x) and x0 = 0.
(A) Calculate the Taylor approximation T3(x)
(B). Use the Taylor theorem to show that
|sin(2x) − T3(x)| ≤ (2/3)(x − x0)^(4).
(C). Write a Matlab program to compute the errors for x = 1/2^(k)
for k = 1, 2, 3, 4, 5, 6, and verify that
|sin(2x) − T3(x)| = O(|x − x0|^(4)).

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 30 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago