Match each of the following functions, f, with p: its (truncated) Taylor polynomial approx- imation about...
2. Find the Taylor polynomial of degree 3 (T3(x)) for each of the following functions with the specified center: (a) f(x) = er at a = 1 (b) f(x) = cos(2.r) at a = ? (c) f(x) = x2 + e + at a = -1
1. (Taylor Polynomial for cos(ax)) For f(x)cos(ar) do the following. (a) Find the Taylor polynomials T(x) about 0 for f(x) for n 1,2,3,4,5 (b) Based on the pattern in part (a), if n is an even number what is the relation between Tn (x) and TR+1()? (c) You might want to approximate cos(az) for all in 0 xS /2 by a Taylor polynomial about 0. Use the Taylor polynomial of order 3 to approximate f(0.25) when a -2, i.e. f(x)...
- x + - - + ... 5. Match the functions (a) – (d) with the Taylor series (1) – (4): (a) V1 + 2x. (1) 1+ 2x + 2x2 + ... 1 (2) 1–+ x2 +.. (c) €22 (3) 1+2 +. (d) e-22 (4) 1 – 2x + 2x2 – ... (b) 21+ 2a
For the function f(x) = e 2x, which of the following polynomials is the 2nd degree Taylor polynomial for f(2') at the point I = 0? 1) P(x) = 1-2+x2 2) P2 (3)=1-23 +22 3) P3(x) = 1 - 2.c + 2x2 4) P4(x) = 1 + 2x + 2x2 O Polynomial in 3) Polynomial in 1) O Polynomial in 2) O Polynomial in 4)
l. (Taylor Polynonial for cos(ar)) Fr f(z) = cos(ar) do the following. (a) Find the Taylor polynomials T.(r) about O for f(x) for n 1,2,3,4,5 (b) Based on the pattern in part (a), if n is an even number what is the relation between T(r) and TR+1(r)? (c) You might want to approximate cs(ar) for all x in。Ś π/2 by a Taylor polynomial about 0. Use the Taylor polynomial of order 3 to approximate f(0.25) when a-2, i.e. f(x)-cos(2x). d)...
Find the Taylor polynomial of order 3 centered at 0. f(x) = com 6-X pg(x) = - * x4 x2 36 + + x3 216 x2 216 + х 36 + + P3(x) = 5 P3(x) = 1296 x3 1296 x4 1296 x2 + 6 36 x3 216 x2 216 P3(x) = х 1 6 + x3 1296 36 Find the quadratic approximation of fat x = 0. f(x) = sin In(2x + 1) P2(x) = 2x + 2x2 p2(x)...
1.f(x)=(2x-3)/(1-x+2x^2), find 4th degreeTaylor polynomial. 2. f(x)=(cos(x)-1)/((sin(x))^2), find 2nd degree Taylor polynomial.
21. Find the derivative of each of the following functions by applying the product rule a. f(x) = (x2 + 1][2x2 + 3x + 4) b. f(x) = x2 cos x c. f(x) = e* sin x 22. Find Find the derivative of each of the following functions by applying the quotient rule a. f(x) = 22+1 f(x) = (2x + 1] / [x - 3] b. f(x) = x+2x+1 3x + 1 c. f(x) = sing 23. Find the...
Problem 2. Write the Taylor series expansion for the following functions up to quadratic terms a. cos (x) about the point x*-pi/4. b. f(xx) 10x1 20x^x2 +10x3 +x 2x 5 about the point (1,1). Compare the approximate and exact values of the function at the point (1.2, 0.8)
5. For each of the rational functions below: 2x + 1 (a) f(x) = x2 (b) g(x) = 2 find 2 + 1 3.12 (c) h(x) = T .x2 - 3.x + 2 (i) the domain of the function (use intervals to give your answers); (ii) all vertical asymptote(s) (if any); (iii) all horizontal asymptote(s) (if any); (iv) all r-intercept(s) (if any); (v) all y-intercept(s) (if any). Write yotir answers in the following table: ydir polynomial domain Vertical Asymptote Horizontal...