Question

1 point) Suppose g is a function which has continuous derivatives, and that g(6)=−1,g′(6)=−3, g′′(6)=3, g′′′(6)=−3...

1 point) Suppose g is a function which has continuous derivatives, and that g(6)=−1,g′(6)=−3, g′′(6)=3, g′′′(6)=−3 .

(a) What is the Taylor polynomial of degree 2 for g near 6? P2(x)=

(b) What is the Taylor polynomial of degree 3 for g near 6? P3(x)=

(c) Use the two polynomials that you found in parts (a) and (b) to approximate g(5.9) .

With P2, g(5.9)≈

With P3, g(5.9)≈

Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
x g(x) g'(x) g''(x) g'''(x) g^(4)(x) 2 17 22 20 14 5 3 50 160/3 141/34...
x g(x) g'(x) g''(x) g'''(x) g^(4)(x) 2 17 22 20 14 5 3 50 160/3 141/34 21 151/8 a) write the third degree taylor polynomial P3 for g(x) at x=3 and use it to approximate g(3.1). Calc permitted b) Use the Lagrange error bound to show that Ig(3.1)-p3(3.1)I<0.0006
(1 point) Find the degree 3 Taylor polynomial T3(x) centered at a=4 of the function f(x)=(7x−20)4/3....
(1 point) Find the degree 3 Taylor polynomial T3(x) centered at a=4 of the function f(x)=(7x−20)4/3. T3(x)= ? True False Cannot be determined The function f(x)=(7x−20)4/3 equals its third degree Taylor polynomial T3(x) centered at a=4. Hint: Graph both of them. If it looks like they are equal, then do the algebra.
​Suppose that the function f(x, y) has continuous partial derivatives fxx, fyy, and fxy at all...
​Suppose that the function f(x, y) has continuous partial derivatives fxx, fyy, and fxy at all points (x,y) near a critical points (a, b). Let D(x,y) = fxx(x, y)fyy(x,y) – (fxy(x,y))2 and suppose that D(a,b) > 0. ​(a) Show that fxx(a,b) < 0 if and only if fyy(a,b) < 0. ​(b) Show that fxx(a,b) > 0 if and only if fyy(a,b) > 0.
Use Newton’s Method to approximate a critical number of the function ?(?)=(1/3)?^3−2?+6. f(x)=1/3x^3−2x+6 near the point...
Use Newton’s Method to approximate a critical number of the function ?(?)=(1/3)?^3−2?+6. f(x)=1/3x^3−2x+6 near the point ?=1x=1. Find the next two approximations, ?2 and ?3 using ?1=1. x1=1 as the initial approximation.
(1 point) Find the degree 3 Taylor polynomial T3(x) of function f(x)=(7x+67)^(5/4) at a=2 T3(x)=?
(1 point) Find the degree 3 Taylor polynomial T3(x) of function f(x)=(7x+67)^(5/4) at a=2 T3(x)=?
i) Approximate the function f(x) = cos x by a Taylor polynomial of degree 3 at...
i) Approximate the function f(x) = cos x by a Taylor polynomial of degree 3 at a = π/3 ii) What is the maximum error when π/6 ≤ x ≤ π/2? (this is the continuation of part i))
6. Suppose that functions f and g and their derivatives with respect to x have the...
6. Suppose that functions f and g and their derivatives with respect to x have the following values at x = 3 X f(x) g(x) f’(x) g’(x) 2 8 2 1 -3 3 1 4 2 4 Find the derivatives with respect to x. √(f(x)g(x)), x = 3 Derivative: ___________________
Suppose that  f   is a twice differentiable function and that its second partial derivatives are continuous....
Suppose that  f   is a twice differentiable function and that its second partial derivatives are continuous. Let  h(t) = f (x(t), y(t))  where  x = 3e ^t  and  y = 2t. Suppose that  fx(3, 0) = 2,  fy(3, 0) = 1,  fxx(3, 0) = 3,  fyy(3, 0) = 2,  and  fxy(3, 0) = 1. Find   d 2h dt 2  when t = 0.
Consider the following function. f(x) = ln(1 + 2x),    a = 1,    n = 3,    0.8 ≤ x ≤...
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)|.
Suppose that  f   is a twice differentiable function and that its second partial derivatives are continuous....
Suppose that  f   is a twice differentiable function and that its second partial derivatives are continuous. Let  h(t) = f (x(t), y(t))  where  x = 2e^ t  and  y = 2t. Suppose that  fx(2, 0) = 1,  fy(2, 0) = 3,  fxx(2, 0) = 4,  fyy(2, 0) = 1,  and  fxy(2, 0) = 4. Find   d ^2h/ dt ^2  when t = 0.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT