1. Find the interval and radius of conv. of In(1-x*) ? 2. without making table find the Mclaurin series for sin'x and e sin 2x?

Q: Assume that sin(x) equals its Maclaurin series for all x. Use the Maclaurin series for sin (5æ?) to…

A: Please see the explanation below

Q: (b) Obtain 3 non zero terms of the Maclaurins series for sin²x. Hence, evaluate sin² x 0.5 1.0.5 5…

A: The given problem is to evaluate the given definite integral using Maclaurin series of sin2x upto 3…

Q: Find the Maclaurin series for the functions sin 3x

A:

Q: 5) Sinh? ( 0.5 )

A:

Q: Use the first three terms of the MacLaurin series for sin(x) to estimate sin(1°), and select the…

A: To find the MacLaurin series for a function f(x), use the following formulae. fx=∑k=0∞fk0k!xk Where…

Q: Find the first four derivatives with respect to x of y = In (1 + sin x). Hence, show that the…

A:

Q: What is the sumation form of the maclaurin series for 1/x*sin(x)? Hint: First find the first few…

A:

Q: Based on known series, give the first four nonzero terms of the Maclaurin series for this function.…

A:

Q: (b) Obtain 3 non zero terms of the Maclaurins series for sin? r. Hence, evaluate 0.5 sin² x dx. Give…

A:

Q: Find a Maclaurin series for f(x) = sin? x.

A:

Q: B- Use power series to evaluate the integral sin.x X -dx

A: We want to find integral of sinx/x using power series.

Q: 10. Given that y = sin-1 2x. Show that (1 - 4x2) d²y = 4x dy dx? dr Find the Maclaurin series for…

A:

Q: Use a power series to compute: sin(x?) dx =

A: We know that power series for sinx is sinx=∑n=0∞(-1)nx2n+1(2n+1)! So, power series for sin(x2) is…

Q: Write the nth term ( general term) for these Maclaurin series  1) (e^x)(cosx) 2)(e^x)(sinx)

A:

Q: In McLauring series of common functions, solve the following. 1. sinh x

A: Maclaurain series of sinhx, using e^x and e^(-x)

Q: Find the Maclourin series of tHe follow. (sinx dx e

A:

Q: Find the Maclaurin series for the functions x sin x

A: Given function is f(x)=xsinx We know that Maclaurin series of sinx is sinx=x-x33!+x55!-x77!+.....…

Q: 4. By using Taylor series, show that e* =cosx+i.sin x.

A:

Q: Assume that sin(x) equals its Maclaurin series for all x. Use the Maclaurin series for sin(4x?) to…

A:

Q: Q: Apply Taylor's expansion and The series for tann at 4

A: Taylor Series expansion of f(x) about the point x=a f(x)=∑k=0∞fk(a)k!(x-a)k…

Q: - Develop the Maclaurin series for cos (2x) eep to terms in X4 what is the greatest truncation error…

A:

Q: Find the first four nonzero terms of the Maclaurin series for f(x) = sin(x^9)cos(x^9).

A: Given the function

Q: Find the first fur.hon yero terms in the Maclaurin Series for sinh x

A:

Q: d E A. By power series, prove that: -cosx = -sinx dx

A:

Q: • Derive the machurin series for f(x) = cesx. Then write down the Equation of the parabola that best…

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: Substitute x 2 for x in the Maclaurin series for sin x.

A: To Substitute x2 for x in the Maclaurin series for sin x

Q: Give McLaurin Series of Cimmon function for sinh x

A: We have to find the Maclurins series of function for fx=sinhx. The Maclurins series of function fx…

Q: 1) Discuss an uniform convergent, continuous ,integral, derivative sinnx for a series E n?

A: Given the series as ∑sinnxn2 First, we will prove that the series converges for all real x, by the…

Q: (i) Find the Maclaurin series for sin x and prove that it represents sin x for all x E R.

A: As per bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: sin-'x= /1 – t²

A:

Q: What is the easiest way to find the Maclaurin series for the function f (x) = sin(x2)?

A:

Q: 10 d sinhx = coshx Q3: A. By power series, prove that: dx

A:

Q: x?e* Use power series to evaluate lim X- 0 cos x -1

A: To evaluate the limit of the given function by using power series expansion.

Q: Write the first 4 nonzero terms of the integral I= x sin(x)dx using the Maclaurin series for sin(y).

A:

Q: Integrate the power series In(1 +x) = (-1)"+1 term-by-term to evaluate Sin(I +x)dx.

A:

Q: obtain the maclaurin's series for the following functions: Sin^2 x

A:

Q: ex-e-* Find Maclaurin series for: 1. sinh x = 2

A: Find your answer below

Q: Use a series representation of sin 3x to find values of r and s for which (sin 3x lim + s) = 0. x2

A:

Q: 5) Find the Maclaurin series for sin X. By using it, show (sin X' lim that as X - 0 equals 1.

A: The Maclaurin series expansion of sin(x) is the Taylor series of sin(x) centred at 0 Also, we need…

Q: Find a Maclaurin series for the given function. 10. f(x) = sin ()

A:

Q: For x > 0, the power series 1 - + * +... + (-1)". x2n + (2n+1)! converges to which of the following?…

A:

Q: ») Does the series S cos(n7) converges or diverges? Vn n=1

A:

Q: Find the first four non-zero terms of the Maclaurin series for the function f (x) = sinh(x²), and…

A: Consider the function fx=sinhx2. Rewrite the given function using sinh(x)=ex-e-x2.

Q: Find the Maclaurin series for the functions sin(x/2)

A: Let the function is:                                        fx=sinx2 Concept used: Maclaurin series…

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: