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(a) Find the fourth degree Taylor polynomial T4(x) for f() = e-64 centered around a =...
(1 point) Find the degree 3 Taylor polynomial T3(x) centered at a = 4 of the function f(x) = (-5x + 24)312]. T3(x) = ? ✓ The function f(x) = (-5x + 24)32) equals its third degree Taylor polynomial T3 (x)/centered at a = 4l. Hint: Graph both of them. If it looks like they are equal, then do the algebra.
3. Approximate the function f(x) = Vx by T4(x), the Taylor polynomial of degree 4 centred at x = 1. Do this in two ways: (a) Use the general formula at the top of page 60--calculating successive derivatives of vx. (b) Change variable so you can directly use the formula of Ex 4.6: 1 17 1/ 11315 (1 + y)1/2 = 1+3y + 2 + - 41 2 y4 + ... ull- 2 2 2 Now we ask how accurate...
We wish to estimate ln(0.5) using an nth degree Taylor polynomial for ln (1 + x) centered at a = 0. How large should n be to guarantee the approximation will be within 0.0001? (Hint: Start by calculating a formula for ∣f (n+1) (z)∣ and finding a bound on this quantity between x = −1/2 and a = 0.)
Find the third Taylor polynomial... (a) Find the third Taylor polynomial T,(x) for f(x)-x at a -1 (b.) Fill in the following table stating your answers to five decimal places T,(x) (from calculator) 2 4 4 (c.) Use Taylor's formula for Rn(x) to estimate the accuracy of the approximation Vr ~ T,(x) when x lies in the interval [T, . (a) Find the third Taylor polynomial T,(x) for f(x)-x at a -1 (b.) Fill in the following table stating your...
16. (a) Approximate f(r)= xlnx by a Taylor polynomial with degree 3 at a=1. (b) Estimate the accuracy of the approximation f (x) T (x) when x lies in the interval 0.5 rs 1.5 17. Find the first three nonzero terms in the Maclaurin series for the function f (x) = --_" and (r+3) its radius of convergence. 16. (a) Approximate f(r)= xlnx by a Taylor polynomial with degree 3 at a=1. (b) Estimate the accuracy of the approximation f...
4) Find the 5th degree Taylor polynomial centered at c = estimate f(1). for the function f(x) = sin I, and use it to Ans Estimate Ts(1.5): Ans Polynomial: 5) A batch of brownies are taken out of a 325°F oven, and placed on the counter in a room kept at a constant 76°F. After 45 minutes, the cookies have cooled to 185°F When will the cookies be 110°F? The differential equation for Newton's Law of Cooling is given by...
1,2,3, and 4 Here are some practice exercises for you. 1. Given f(x) e2, find the a. Maclaurin polynomial of degree 5 b. Taylor polynomial of degree 4 centered at 1 c. the Maclaurin series of f and the interval of convergence d. the Taylor series generated by f at x1 2. Find the Taylor series of g(x) at x1. 3. Given x -t2, y t 1, -2 t1, a. sketch the curve. Indicate where t 0 and the orientation...
Find T5(a): Taylor polynomial of degree 5 of the function f(x) = cos(x) at a = T5(x) = Using the Taylor Remainder Theorem, find all values of x for which this approximation is within 0.001774 of the right answer. Assume for simplicity that we limit ourselves to a < 1. nial of degree 5 of the function f(x) = cos(x) at a = 0.
Q. f(n) = tan (n) 1) Compute degree - 2 Taylor Polynomial of f(n) centered at ua Je 4 (2) Use the Taylo Polynomial computed to estimate to stimete ! tau (I + 0.1). 3) using the fact that If(x) <3 for o excit tool show to that tapeeestarte 4 the estimate in part (2) is correct to within an error of 0.0005. f(n) = tan (1) To a) Compute the degree a Taylor - Polynomial of fin) centered at...
plz show work 1. (a) Find T5(x), the Taylor polynomial of degree 5, for Inx centered at x = 1. (b) Evaluate Ts (3). How close is its value to In 3? (c) The interval of convergence for the Taylor series of In x centered at x= 1 is (0,2). Use the fact that Inx= - In to find a different value of x to use in Ts(x) to approximate In 3. How close is your approximation? 2. Long ago,...