Let F(x) = si sin (6t²) dt. Find the MacLaurin polynomial of degree 7 for F(x). 27³-27 2x3 + 324 11. 55 64815 175 0.77 Use this polynomial to estimate the value of for sin (62²) dx. 1.0344113455375 X X

Q: plot the function f(x)=x*sin(x)-cos(x) to show that it has one root at the interval [0,pi/2]

A: The given function is  defined in the closed interval .We shall fill the following tabular column.…

Q: How do you know that the functions sin x, ln x, and ex are not polynomials? Give reasons for your…

A: Polynomials have finite terms. And it has a highest degree.  But sinx , lnx and ex have infinite…

Q: 2. If f(g(x)) = sin x + 3sinx - 1, determine possible expressions for f(x) and g(x), where g(x) # x.

A: (1st method/way): Let f(x)=x²+3x-1 and g(x)=sinx Then we can find f(g(x)) as follows…

Q: Evaluate S₁ 45 dx 1- cos (9x)

A: To evaluate .

Q: Adobe Reader uch 2. Find the maximum and minimum values of f(x) = cos? a – values of a do the…

A: According to the question, we need to determine the maxima and minima for the trigonometric…

Q: Which function is obtain by shifting the graph of f(t) = sin 3t a distance of 3Tt/2 units to the…

A: Given f(t) = sin(3t)  A shift of a units to the right of t axis is given by  f(t-a)  Thus a shift of…

Q: Verify that f′(x) = g′(x) and explain the relationship between f and g.

A: We have given fx=sin x-3xx, gx=sin x+2xx We have to verify f'x=g'x Quotient rule:…

Q: 1. Prove that the derivative of tan(x) is sec²(x) directly from the definition of the derivative.…

A:

Q: √√3 tan-¹x 4. (10 points) Evaluate SY 1+x2 dx (using substitution).

A: The value of the integral is 7 pi^2 / 288.

Q: Find the exact values of x in the interval [0, 3pie] that satisfy the equation sinx= -1/2

A:

Q: Consider the function f(x) = sin2 (x) − sin(x), 0 ≤ x ≤ 2π.    Find the intervals of increase and…

A: Consider the function f(x) = sin2(x) − sin(x), 0 ≤ x ≤ 2π.  Find the intervals of increase and…

Q: X Let F(x) = ²* sin(6t²) dt. Find the MacLaurin polynomial of degree 7 for F(x). Use this polynomial…

A:

Q: 1. Differentiate the following functions a. f(x) = sin(x) cos(x)

A: According to bartleby guidelines we supposed to do the first one of multiple questions kindly repost…

Q: 3. Evaluate f x sin2 (x²) dx.

A: Given I=∫x sin2x2 dx To Find I

Q: Find the relative minimum and maximum value of the function: ƒ(x) = 8 cos²(x) – 8√3 sin(x) over the…

A:

Q: Differentiate the function.  f(x)=cos{sin(tan(pi*x))}1/2

A: Given f(x)=cos{sin(tan(pi*x))}1/2

Q: Q5: Find for the following functions: (4) y = x sinh 2x-cosh 2x (2) y = tan³√cot(7x) ; (3) y = sin²…

A: Sol:- (2) ddxtan3cot7x Apply the chain rule =3tancot7x2ddxtancot7x

Q: Differentiate the given function. y=XV8X-5 y'= (Type an exact answer, using radicals as needed.)

A:

Q: of of and da For the function f(t,a) = sin (8rt + 7a), find %3D - at

A:

Q: Find for the following functions: (4) y = x sinh 2x --cosh 2x (2) y = tan³√/cot(7x); (3) y= sin Imvr

A:

Q: Let ƒ(x) = 4x − sin(4x). a) Find f (0). f(0) = b) Find ƒ(§). ƒ(§) = CHECK ANSWER

A: Given query is to find the value of the function at indicated points.