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mathematics
precalculus

Questions and Answers of Precalculus

Use multiplication or division of power series to find the first three nonzero terms in the Maclaurin series for each function.y = ex sin2 x
Use multiplication or division of power series to find the first three nonzero terms in the Maclaurin series for each function.y = (arctan x)2
Use series to evaluate the limit. .3 -1 3x + 3 tanx lim .5
Use series to evaluate the limit. V1 + x - 1– x х? lim х—0 х .2 1/2
Use series to evaluate the limit. 1- cos x lim x0 1 + x – e e*
Use series to approximate the definite integral to within the indicated accuracy.
Use series to approximate the definite integral to within the indicated accuracy.(four decimal places) | sin(x*) dx
Use series to approximate the definite integral to within the indicated accuracy.(four decimal places) 1/2 arctan x dx
Evaluate the indefinite integral as an infinite series. arctan(x?) dx
Evaluate the indefinite integral as an infinite series. cos x – 1 dx х
Evaluate the indefinite integral as an infinite series. х? sin (x?) dx
Evaluate the indefinite integral as an infinite series. V1 + x³ dx
Use the Maclaurin series for ex to calculate 1/10√e 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
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
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
Use a Maclaurin series in Table 1 to obtain the Maclaurin series for the given function. x – sin x if x + 0 .3 x3 | f(x) = if x = 0 1/6
Use a Maclaurin series in Table 1 to obtain the Maclaurin series for the given function. f(x) = sin?x sin?x = (1 1 – cos 2x)
Use a Maclaurin series in Table 1 to obtain the Maclaurin series for the given function. .2 х* f(x) = V2 + x
Use a Maclaurin series in Table 1 to obtain the Maclaurin series for the given function. f(x) = V /4+x2
Use a Maclaurin series in Table 1 to obtain the Maclaurin series for the given function. + x³) = x² In(1 f(x)
Use a Maclaurin series in Table 1 to obtain the Maclaurin series for the given function. ,2х — е2м f(x) — е3н -
Use a Maclaurin series in Table 1 to obtain the Maclaurin series for the given function.f (x) = x cos 2x
Use a Maclaurin series in Table 1 to obtain the Maclaurin series for the given function. f(x) = sin(7x/4)
Use a Maclaurin series in Table 1 to obtain the Maclaurin series for the given function.f (x) = arctan (x2)
Use the binomial series to expand the function as a power series. State the radius of convergence.
Use the binomial series to expand the function as a power series. State the radius of convergence.3√8 + x
Prove that the series obtained in Exercise 18 represents cosh x for all x.
Prove that the series obtained in Exercise 17 represents sinh x for all x.
Prove that the series obtained in Exercise 25 represents sin x for all x.
Prove that the series obtained in Exercise 13 represents cos x for all x.
Find the Taylor series for f (x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.] Also find the associated radius of convergence. f(x) =
Find the Taylor series for f (x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.] Also find the associated radius of convergence. f(x) =
Find the Taylor series for f (x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.] Also find the associated radius of convergence. f(x) )
Find the Taylor series for f (x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.] Also find the associated radius of convergence. 2х f(x)
Find the Taylor series for f (x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.] Also find the associated radius of convergence. f(x) =
Find the Taylor series for f (x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.] Also find the associated radius of convergence. |f(x) =
Find the Taylor series for f (x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.] Also find the associated radius of convergence. f(x) =
Find the Taylor series for f (x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.] Also find the associated radius of convergence. f) —
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) → 0.] Also find the associated radius of
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) → 0.] Also find the associated radius of
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) → 0.] Also find the associated radius of
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) → 0.] Also find the associated radius of
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) → 0.] Also find the associated radius of
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) → 0.] Also find the associated radius of
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) → 0.] Also find the associated radius of
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) → 0.] Also find the associated radius of
Use the definition of a Taylor series to find the first four nonzero terms of the series for f (x) centered at the given value of a.f (x) = cos2x, a = 0
Use the definition of a Taylor series to find the first four nonzero terms of the series for f (x) centered at the given value of a. sin x, а 3D п/6 f(x) —
Use the definition of a Taylor series to find the first four nonzero terms of the series for f (x) centered at the given value of a.f (x) = ln x, a = 1
Use the definition of a Taylor series to find the first four nonzero terms of the series for f (x) centered at the given value of a. f(x) = Vx, a = 8
Use the definition of a Taylor series to find the first four nonzero terms of the series for f (x) centered at the given value of a. f(x) : a = 2 1 +x' (х)
Use the definition of a Taylor series to find the first four nonzero terms of the series for f (x) centered at the given value of a.f (x) = xex, a = 0
Find the Taylor series for f centered at 4 ifWhat is the radius of convergence of the Taylor series? (-1)"п! 3"(п + 1) fm(4)
The graph of f is shown.(a) Explain why the seriesis not the Taylor series of f centered at 1.(b) Explain why the seriesis not the Taylor series of f centered at 2. y A 1 х 1.6 – 0.8(x – 1) +
Show that the functionis a solution of the differential equation
Use a power series to approximate the definite integral to six decimal places. r0.3 dx 1 + x4
Use a power series to approximate the definite integral to six decimal places. r0.2 хIп x In(1 + х?) dx
Use a power series to approximate the definite integral to six decimal places. C1/2 arctan(x/2) dx
Use a power series to approximate the definite integral to six decimal places. r0.3 dx 1 + x3
Evaluate the indefinite integral as a power series. What is the radius of convergence? tan'x dx х
Evaluate the indefinite integral as a power series. What is the radius of convergence? dt 1 + t3
Find a power series representation for f , and graph f and several partial sums sn(x) on the same screen. What happens as n increases?f (x) = tan-1(2x)
Find a power series representation for f , and graph f and several partial sums sn(x) on the same screen. What happens as n increases?f (x) = ln(1 + x4)
Find a power series representation for f , and graph f and several partial sums sn(x) on the same screen. What happens as n increases?f (x) = x2/x2 + 1
Find a power series representation for the function and determine the radius of convergence.f (x) = x2 + x/(1 - x)3
Find a power series representation for the function and determine the radius of convergence.f (x) = 1 + x/(1 - x)2
Find a power series representation for the function and determine the radius of convergence.f (x) = (x/2 - x)3
Find a power series representation for the function and determine the radius of convergence.f (x) = x/(1 + 4x)2
Find a power series representation for the function and determine the radius of convergence.f (x) = x2 tan-1(x3)
Express the function as the sum of a power series by first using partial fractions. Find the interval of convergence. 2x + 3 f(x) x? + 3x + 2
Express the function as the sum of a power series by first using partial fractions. Find the interval of convergence. 2х — 4 f(x) = х* x? — 4х + 3
Find a power series representation for the function and determine the interval of convergence. х+а f(x) = a > 0 x2 + a?'
Find a power series representation for the function and determine the interval of convergence. х — 1 f(x) 2 х+
Find a power series representation for the function and determine the interval of convergence. х f(x) : 2x2 + 1
Find a power series representation for the function and determine the interval of convergence. f(x) = x* + 16 16
Find a power series representation for the function and determine the interval of convergence. 4 f(x) 2х + 3
Find a power series representation for the function and determine the interval of convergence. 2 f(x) 3 — х
Find a power series representation for the function and determine the interval of convergence. 5 |f(x) = 2 1- 4x?
Find a power series representation for the function and determine the interval of convergence. f(x) 1 + x
Find the radius of convergence and interval of convergence of the series. (2x – 1)" 5"/n n-1
If 0, " style="" class="fr-fic fr-dib">find the interval of convergence of the series and a formula for f(x). f(x) = E-o Cnx", where cn+4 00 N3D0 C, for all n > 0,
Let p and q be real numbers with p < q. Find a power series whose interval of convergence is(a) [p, q] (b) [p, q] (c) [p, q] (d) [p, q]
Find the radius of convergence and interval of convergence of the series.
Find the radius of convergence and interval of convergence of the series.
Find the radius of convergence and interval of convergence of the series. in Σ 1: 3· 5· ...• (2n – 1) (2n – 1) n-1 8.
Find the radius of convergence and interval of convergence of the series. 2η Σ n(In n)² η-2
Find the radius of convergence and interval of convergence of the series.
Find the radius of convergence and interval of convergence of the series.
Find the radius of convergence and interval of convergence of the series.
Find the radius of convergence and interval of convergence of the series. b" (х — а)", In n b>0 п-2
Find the radius of convergence and interval of convergence of the series. 0 л п-1
Find the radius of convergence and interval of convergence of the series. (х — 2)" in п" л—1
Find the radius of convergence and interval of convergence of the series.
Find the radius of convergence and interval of convergence of the series. (х + 2)" 2" In n л—2
Find the radius of convergence and interval of convergence of the series.
Find the radius of convergence and interval of convergence of the series. r2n n-1 n!
Find the radius of convergence and interval of convergence of the series. п x" х" Σ 2"(n² + 1) 2"( п—1
Find the radius of convergence and interval of convergence of the series.
Find the radius of convergence and interval of convergence of the series. (-1)"4" х* л—1 п

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