3 = (d) tan M 11 = (1 km x 40 T La Sec (2/2) 12 ½/2 lim 늘 x46 TTT 1 sec ² (²/₂) 1⁄2 sec² (0) = 1/2 x ² = 1½/2 ******** - Starting from first principles, find the first three non-zero terms of the Maclaurin series for the function f(x)=(1+x)¹².

Q: 5. (a) Compute the sine series for f(x) = et on [0, 7]. You may use an integral calculator, but be…

A:

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: (-1)" 2n+1 Use the power series sin x=E; to approximate (by using four terms) the value of (2n+1)!"…

A: Let's replace x by x2 to obtain: Let's now expand up to four terms to get:

Q: 11. (a) State the Taylor series at 0 for cos(x). Then using the appropriate shortcut, modify this…

A:

Q: 18 Given the power series F(x)= 2 (-1)" (x-3)" n= 0 2" Find the derivative for the power series…

A: Answer to the question as follows:

Q: sinx x0 e²x-1 5. Use power series to evaluate lim

A: Power series expansion

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

A:

Q: (2) Find a power series for the function centered at 0. 3 1 (x + 1)² 1 (x + 1)³ (a) f(x) = (b) f(x)…

A: Taylor series about x=0,

Q: 4. Use the Alternating Series Error Theorem to estimate f₁ cos(x²) dx with an error of less than…

A: Step 1:Step 2:Step 3:

Q: Q2:Find the odd sine series of this function al E Note: (end at n=l ...) F(x) = 3x + x niversity…

A: Given function is F(x)=3x2+x , 0<x<π find sine series of the given function  F(x)=∑n=1∞ bn…

Q: (b) Use the first four terms of a power series you found in part (a) to approximate the value of |…

A: The answer is found in step-2

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: 4) (a) Find a deqree 3 power series for the function sin(x) centered at T fla) = f (2) + f(a) (x-a)…

A:

Q: 5. Let f(x) = -1 0<x<T 0 π < x < 2π 1 2π <x<3π (a) Find the sin series for f(r) with period 67. (b)…

A: 5) (a)

Q: Find the power series of the function f(z) = sin(2z) with centre 7/3. Find the power series of the…

A: We will use taylor series at x=a The Taylor series of a real or complex-valued function f (x) that…

Q: dy 1 ( +2)(y– 1)² For the differential equation dx 2 a. Sketch the direction field where -2<x<2 and…

A: Hi! You have posted multiple subparts. We have solved the first two subparts. If you need an answer…