72. Find f(7) (0) and ƒ(8) (0) for f(x) = tan¹ x using the Maclaurin series.

Q: Using the fact that f(x) = ₁¹² = Σox" for |x| < 1 represent function g(x) = 5²+1 as a power series.

A:

Q: (b) Find the Taylor's series generated by the following function at x = a = 2 f(x) =x' – 2.x+ 4.

A: Given that, fx=x3-2x+4 Given point is x=a=2

Q: Consider the function given by the following power series. Зп + 1 f(x) = Σ (x+ 2)3n п! n=0 Find the…

A: Given power series for the function fx is fx=∑n=0∞3n+1n!x+23n

Q: (b) Expand f(x) = x as a sine series in the half interval (0, L). Sketch the series you have found…

A: To expand  f(x) = x  as a sine series in the half-interval (0, L), we can use the standard technique…

Q: 6. Find the Maclaurin series for g(x) S™ g(t) dt. = cos x - 1 + −1+1/2/22 x² and h(r) =

A: The above series is the Maclaurins series for g(x).

Q: Find f x² sin(x²) dx using the Maclaurin Series.

A:

Q: ". Expand the function f(x)=|x, - T < x < A in an appropriate cosine or sine series.

A: Given that, fx=x ,  -π&lt;x&lt;π  Here, -L , L=-π,π Hence, L=π As the given function is even…

Q: Find the 3rd degree Maclaurin Polynomial for f(x) = 2". d -b² = In(b) · b². dx Recall that T3(x)…

A: We will use the basic knowledge of derivatives and the McLaurin series to answer all the three parts…

Q: 6. Find the sine series of Sx, f(x) 0 <x < #/2 - x, T/2 < x < T

A:

Q: Consider f(x) = 1 – x for 0 1: an b) O an = c) O ao = 1/2, and for n > 1: a, = 4(1+…

A:

Q: Find a power series representation for the function X f(x) = 9+x² and determine the radius of…

A:

Q: 2. Find a power series representation for f(x) correct to 6 decimal places. 0.1 602; = X 1+x³ x…

A:

Q: Observe the function X f(x) = (1+2x)² In order to find the power series for this function, complete…

A:

Q: Q4: Find the Mackurin series for function f(x)=Jx+1

A: Given function: fx=x+1 To write: The Maclaurin series for the function fx. Formula used: The formula…

Q: Let the improper integrals " sin(-)dx and sin?()dx (i) Write down the first 3 terms of Maclaurin…

A:

Q: 1. Expand f(x) = π 0 if 0 < x < 2² ㅠ if <x< ₁ π, 1 if in a half-range: (a) Sine series. (b) Cosine…

A: The function is defined by fx=0if 0&lt;x&lt;π21if π2&lt;x&lt;π We have to evaluate the half range…

Q: Use your knowledge of the Maclaurin series for f(x) = e" to find the Maclaurin series for g(x) =…

A:

Q: Use the Maclaurin series for function f(x) = tan-¹ x to find the first four nonzero terms of the…

A: (a). Given that the function is                                 f(x)=tan-1(x).      To find the the…

Q: Given the function f(x) = (÷) (a) Find a power-series representation for f(x). Σ п(п +1) (п + 2)!…

A:

Q: 1. You are given that tan-1 x = x-x3 +x 5 – ÷x' + …· for |x| <1. Use the given series to obtain a…

A: (a)-According to question given thattan-1(x)=x-13x3+15x5-17x7+.... for |x|&lt;1Let f(x)=tan-1xNow…

Q: 1. Given that f (x) = 2, find f(m) (0) using Maclaurin series.

A:

Q: Q5. Let the improper integrals, sin()dx and sin² ()dx (i) (ii) Write down the first 3 terms of…

A: Introduction: Sometimes the Maclaurin series is very efficient to integrate a function. The power…

Q: (a) Find the Taylor's series for the function f(x)= sin x at x = (b) Using L'Hospital 'rule to find…

A:

Q: Wants to know what will be the Maclaren series of g(x) = sin(x) is ?

A: Maclaurin series of function fx is a Taylor series of function fx at: a=0…

Q: Find the Maclaurin series for f(x) = ex+x² using the familiar series. Then use the results to…

A: We know the series of ex=1+x+x22!+x33!+…

Q: Find the first 5 terms in the power series representation for f(x). S(x)= [e*dx

A: handwriting solution

Q: 5. Find the sine series of 0 < x < T/2 Sx, f(x) T – x, T/2 <x<

A: Fourier series

Q: 2. Define functions sinh(x) and cosh(x) as follows: sinh(r) = = e-e 2 e² + ex and cosh(): = 2 These…

A: Approach to solving the question: Detailed explanation: Examples: Key references:

Q: Let f(x) = cos (3x²) - 1 x² = Evaluate the 10th derivative of f at x = 0. f(10) (0) = Free-form Snip…

A:

Q: Given that f(x) = 2, find f(m) (0) using Maclaurin series.

A:

Q: 8. One of the fastest series for (T/4) is: 1 + 2 tan 8 1 =6 tan- 4 + tan 57 239 Use the series below…

A: