2.99 See Answer

Question: Use a Maclaurin series in Table 1

Use a Maclaurin series in Table 1 to obtain the Maclaurin series for the given function.
Use a Maclaurin series in Table 1 to obtain the Maclaurin series for the given function.





Transcribed Image Text:

sin x if x+0 f(x) = if x = 0


> Find the indicated power using De Moivre’s Theorem. (1 – √3 i)5

> Find the indicated power using De Moivre’s Theorem. (1 + i)20

> Find polar forms for zw, z/w, and 1/z by first putting z and w into polar form. = 4(/3 + i), w = -3 – 3i

> Find polar forms for zw, z/w, and 1/z by first putting z and w into polar form. z = 2/3 – 2i, w = -1 +i

> Find polar forms for zw, z/w, and 1/z by first putting z and w into polar form. z = 4/3 – 4i, w = 8i %3D %3D

> Find polar forms for zw, z/w, and 1/z by first putting z and w into polar form. z = 3 + i, w = 1 + v3i

> Find the area of the region that lies inside the first curve and outside the second curve. r=1- sin 6, r= 1

> Write the number in polar form with argument between 0 and 2π. 8i

> Write the number in polar form with argument between 0 and 2π. 3 + 4i

> Write the number in polar form with argument between 0 and 2π. 1 – √3 i

> Write the number in polar form with argument between 0 and 2π. -3 + 3i

> Find all solutions of the equation. z2 + 1/2 z + 1/4 = 0

> Find all solutions of the equation. z2 + x + 2 = 0

> Find all solutions of the equation. 2x2 – 2x + 1 = 0

> Find all solutions of the equation. x2 + 2x + 5 = 0

> Find all solutions of the equation. x4 = 1

> Find all solutions of the equation. 4x2 + 9 = 0

> Find the area of the region that lies inside the first curve and outside the second curve. r= 2 cos e, r = 1

> Prove the following properties of complex numbers. (a) z + w = 7 + w (b) zw m = mz (q) (c) z* = 7", where n is a positive integer [Hint: Write z = a + bi, w = c + di.]

> Find the complex conjugate and the modulus of the number. -4i

> Find the complex conjugate and the modulus of the number. -1 + 2/2 i

> Find the complex conjugate and the modulus of the number. 12 – 15i

> Evaluate the expression and write your answer in the form a + bi. V-3V-12

> Evaluate the expression and write your answer in the form a + bi. V-25

> Evaluate the expression and write your answer in the form a + bi. i100

> Evaluate the expression and write your answer in the form a + bi. i3

> Evaluate the expression and write your answer in the form a + bi. 3 4 — Зі 3.

> Evaluate the expression and write your answer in the form a + bi. 1 1+ i

> Find the area of the region enclosed by one loop of the curve. r= 2 cos e - sec e

> Evaluate the expression and write your answer in the form a + bi. 3 + 2i 1- 4i

> Evaluate the expression and write your answer in the form a + bi. 1+ 4i 3 + 2i

> Evaluate the expression and write your answer in the form a + bi. 21(를 - 1)

> Evaluate the expression and write your answer in the form a + bi. 12 + 7i

> Evaluate the expression and write your answer in the form a + bi. (1 — 21)(8 — 3і)

> Evaluate the expression and write your answer in the form a + bi. (2 + 5i)(4 – i)

> Evaluate the expression and write your answer in the form a + bi. (4 – 41) – (9 + 31)

> Evaluate the expression and write your answer in the form a + bi. (5 – 6i) + (3 + 2i)

> Evaluate the indefinite integral as an infinite series. f ex – 1/x, dx

> Evaluate the indefinite integral as an infinite series. f x cos (x3) dx

> Find the area of the region enclosed by one loop of the curve. r=1+ 2 sin e (inner loop)

> For the limit illustrate Definition 1 by finding values of that correspond to e = 0.5 and e = 0.1 e* - 1 lim - 1

> Find a power series representation for the function and determine the interval of convergence. x? f(x) = .3 a - x .3

> (a). Use the binomial series to expand 1/ √1 - x2. (b). Use part (a) to find the Maclaurin series for sin-1 x.

> Use the Maclaurin series for sin x to compute si 30 correct to five decimal places.

> Use the Maclaurin series for ex to calculate e-0.2 correct to five decimal places.

> Find the Maclaurin series of f (by any method) and its radius of convergence. Graph f and its first few Taylor polynomials on the same screen. What do you notice about the relationship between these polynomials and f? f(x) = In(1 + x²)

> If the radius of convergence of the power series ∑∞n=0cnxn is 10, what is the radius of convergence of the series ∑∞n=0ncnxn-1? Why?

> Let fn(x) = (sin nx)/n2. Show that the series ∑fn(x) converges for all values of x but the series of derivatives ∑fn'(x) diverges when x = 2nπ, an integer. For what values of x does the series ∑fn"(x) converge?

> Find the Maclaurin series of f (by any method) and its radius of convergence. Graph f and its first few Taylor polynomials on the same screen. What do you notice about the relationship between these polynomials and f? f(x) = cos(x²)

> Find the area of the region enclosed by one loop of the curve. r= 4 sin 30

> Use a Maclaurin series in Table 1 to obtain the Maclaurin series for the given function. .2 f(x) = /2 + x

> Use a Maclaurin series in Table 1 to obtain the Maclaurin series for the given function. f(x) = - V4 + x? %3D

> The resistivity of a conducting wire is the reciprocal of the conductivity and is measured in units of ohm-meters (Ωm). The resistivity of a given metal depends on the temperature according to the equation where is the temperature i

> An electric dipole consists of two electric charges of equal magnitude and opposite sign. If the charges are q and -q and are located at a distance d from each other, then the electric field E at the point P in the figure is E = q/D2 –

> Use a Maclaurin series in Table 1 to obtain the Maclaurin series for the given function. f(x) — е* + 2е- e

> Use a Maclaurin series in Table 1 to obtain the Maclaurin series for the given function. f(x) = e + e2*

> Suppose you know that and the Taylor series of f centered at 4 converges to f (x) for all in the interval of convergence. Show that the fifth degree Taylor polynomial approximates f (5) with error less than 0.0002. (-1)*n! f®(4) 3"(n 1)

> Use a Maclaurin series in Table 1 to obtain the Maclaurin series for the given function. f(x) = sin 7x

> Use the binomial series to expand the function as a power series. State the radius of convergence. (1 – x)-/3

> Use the Alternating Series Estimation Theorem or Taylor&acirc;&#128;&#153;s Inequality to estimate the range of values of for which the given approximation is accurate to within the stated error. Check your answer graphically. x (| error |< 6 :0.01)

> Find the area of the region enclosed by one loop of the curve. r= sin 20

> Use the binomial series to expand the function as a power series. State the radius of convergence. 1 (1 + x)* 4

> Use the binomial series to expand the function as a power series. State the radius of convergence. + x

> Use the information from Exercise 14 to estimate sin 380 correct to five decimal places. Exercise 14: f(x) = sin x, a = "/6, n= 4, 0<x</3

> Use the information from Exercise 5 to estimate cos 800 correct to five decimal places. Exercise 5: Find the Taylor polynomial T3(x) for the function f at the number a. Graph f and T3 on the same screen. = cos x, a = T/2 1 = 7/2

> (a). Approximate f by a Taylor polynomial with degree n at the number a. (b). Use Taylor&acirc;&#128;&#153;s Inequality to estimate the accuracy of the approximation f (x) &acirc;&#137;&#136; Tn (x) when x lies in the given interval. (c). Check your resu

> (a). Approximate f by a Taylor polynomial with degree n at the number a. (b). Use Taylor&acirc;&#128;&#153;s Inequality to estimate the accuracy of the approximation f (x) &acirc;&#137;&#136; Tn (x) when x lies in the given interval. (c). Check your resu

> (a). Approximate f by a Taylor polynomial with degree n at the number a. (b). Use Taylor&acirc;&#128;&#153;s Inequality to estimate the accuracy of the approximation f (x) &acirc;&#137;&#136; Tn (x) when x lies in the given interval. (c). Check your resu

> (a). Approximate f by a Taylor polynomial with degree n at the number a. (b). Use Taylor&acirc;&#128;&#153;s Inequality to estimate the accuracy of the approximation f (x) &acirc;&#137;&#136; Tn (x) when x lies in the given interval. (c). Check your resu

> (a). Approximate f by a Taylor polynomial with degree n at the number a. (b). Use Taylor&acirc;&#128;&#153;s Inequality to estimate the accuracy of the approximation f (x) &acirc;&#137;&#136; Tn (x) when x lies in the given interval. (c). Check your resu

> (a). Approximate f by a Taylor polynomial with degree n at the number a. (b). Use Taylor&acirc;&#128;&#153;s Inequality to estimate the accuracy of the approximation f (x) &acirc;&#137;&#136; Tn (x) when x lies in the given interval. (c). Check your resu

> Graph the curve and find the area that it encloses. r= 2 sin e + 3 sin 90

> (a). Approximate f by a Taylor polynomial with degree n at the number a. (b). Use Taylor&acirc;&#128;&#153;s Inequality to estimate the accuracy of the approximation f (x) &acirc;&#137;&#136; Tn (x) when x lies in the given interval. (c). Check your resu

> (a). Approximate f by a Taylor polynomial with degree n at the number a. (b). Use Taylor&acirc;&#128;&#153;s Inequality to estimate the accuracy of the approximation f (x) &acirc;&#137;&#136; Tn (x) when x lies in the given interval. (c). Check your resu

> Find the Maclaurin series for f (x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that Rn (x) &acirc;&#134;&#146; 0.] Also find the associated radius of convergence. f(x) = xe хе

> Find the Maclaurin series for f (x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that Rn (x) &acirc;&#134;&#146; 0.] Also find the associated radius of convergence. f(x) = e5=

> Find the Taylor polynomial T3(x) for the function f at the number a. Graph f and T3 on the same screen. f(x) = tan-'x, a = 1

> Find the Taylor polynomial T3(x) for the function f at the number a. Graph f and T3 on the same screen. f(x) %3D хе -2:, а %3D 0 = xe a = 0

> Find the Taylor polynomial T3(x) for the function f at the number a. Graph f and T3 on the same screen. f(x) In x a = 1

> Find the Taylor polynomial T3(x) for the function f at the number a. Graph f and T3 on the same screen. = cos x, a = T/2 1 = 7/2

> Find the Taylor polynomial T3(x) for the function f at the number a. Graph f and T3 on the same screen. f(x) = x + e, a=0

> Find the Taylor polynomial T3(x) for the function f at the number a. Graph f and T3 on the same screen. f(x) = 1/x, a = 2

> Graph the curve and find the area that it encloses.

> (a). Find the Taylor polynomials up to degree 3 for f (x) = 1/x centered at a = 1. Graph f and these polynomials on a common screen. (b). Evaluate f and these polynomials at x = 0.9 and 1.3. (c). Comment on how the Taylor polynomials converge to f (x).

> (a). Find the Taylor polynomials up to degree 6 for f (x) = cos x centered at a = 0. Graph f and these polynomials on a common screen. (b). Evaluate f and these polynomials at x = π/4, π/2, and π. (c). Comment on how the Taylor polynomials converge to f

> Use series to evaluate the following limit. limx→0 sin x – x/ x3

> (a). Approximate f by a Taylor polynomial with degree at the number a. (b). Graph f and Tn on a common screen. (c). Use Taylor&acirc;&#128;&#153;s Inequality to estimate the accuracy of the approximation f (X) = Tn(x) when lies in the given interval. (d)

> (a). Approximate f by a Taylor polynomial with degree at the number a. (b). Graph f and Tn on a common screen. (c). Use Taylor&acirc;&#128;&#153;s Inequality to estimate the accuracy of the approximation f (X) = Tn(x) when lies in the given interval. (d)

> Use series to approximate f10√1 + x4, dx correct to two decimal places.

> Evaluate f ex/x dx as an infinite series.

> Find the Maclaurin series for f and its radius of convergence. You may use either the direct method (definition of a Maclaurin series) or known series such as geometric series, binomial series, or the Maclaurin series for ex, sin x, and tan-1x. f(x)

> Find the Maclaurin series for f and its radius of convergence. You may use either the direct method (definition of a Maclaurin series) or known series such as geometric series, binomial series, or the Maclaurin series for ex, sin x, and tan-1x. f(x)

> Find the Maclaurin series for f and its radius of convergence. You may use either the direct method (definition of a Maclaurin series) or known series such as geometric series, binomial series, or the Maclaurin series for ex, sin x, and tan-1x. f(x)

> Sketch the curve and find the area that it encloses. r = 2 + cos 2θ

> Find the Maclaurin series for f and its radius of convergence. You may use either the direct method (definition of a Maclaurin series) or known series such as geometric series, binomial series, or the Maclaurin series for ex, sin x, and tan-1x. f(x)

> Find the Maclaurin series for f and its radius of convergence. You may use either the direct method (definition of a Maclaurin series) or known series such as geometric series, binomial series, or the Maclaurin series for ex, sin x, and tan-1x. f(x)

> Find the Maclaurin series for f and its radius of convergence. You may use either the direct method (definition of a Maclaurin series) or known series such as geometric series, binomial series, or the Maclaurin series for ex, sin x, and tan-1x. f(x)

> Find the Maclaurin series for f and its radius of convergence. You may use either the direct method (definition of a Maclaurin series) or known series such as geometric series, binomial series, or the Maclaurin series for ex, sin x, and tan-1x. f(x)

> Find the Maclaurin series for f and its radius of convergence. You may use either the direct method (definition of a Maclaurin series) or known series such as geometric series, binomial series, or the Maclaurin series for ex, sin x, and tan-1x. x? f

> Find the Taylor series of f (x) = cos x at a = π/3.

2.99

See Answer