The best approximation of f (x) = cos(3 + x) by a %3D Fourier polynomial of degree 1 is 1) F(x) = cos(3 + x) 2) F(x) = cos x + sin 3) F(x) = cos 3 cos x – sin 3 sin x 4) F(x) = 3 cos x. 5) F(x) = sin 3 sin x.

Q: 3. The integral of sin24x cos4x dx is a. (1/4) sin³ 4x + C b. (1/3) sin³ 4x +C c. (1/12) sin³ 4x+ C…

A:

Q: Evaluate the integral: cos 4x cos 6x dx. A) sin 2x + sin 10x + c. 20 -sin 2x + sin 10x + c. C) sin…

A: Let's find integration of given function.

Q: Evaluate [(1 +x-3 + sin4x)dx -2 cos4x X - + c 4 0x-- cos4x + C cos4x O 2x- 4 0 4x-두-5t +c cos5x + c…

A: As we know that the integration of : ∫fx±gxdx=∫fxdx±∫gxdx ∫xndx=xn+1n+1+c ∫sinxdx=-cosx+c

Q: 11. Evaluate f- 2 sin 3x dx 4+cos 3x a.) -2 In 14+cos3x| + C b.) 3 In 14+cos3x| + C c.) - In…

A: Solve by integration

Q: Find all solutions to cos(7x)−cos(x)=sin(4x)cos(7x)-cos(x)=sin(4x) on 0≤x<2π30≤x<2π3

A: We know, cos(a)-cos(b)= -2sin(a+b)/2*sin(a-b)/2....(i)

Q: | cos(5x) sin(13x)dx = 1 sin(&x) ) sin(18x 4 6. OB. - 5 sin(5x) sin(13x) + 13 cos(5x) 1 cos(1&x)…

A:

Q: We use the BISECTION METHOD to find the root of this nonlinear functional e = sin(x) +x². x' In(x)…

A:

Q: 16. Use Theorem 12 to show that 2n r=0

A:

Q: Find the exact error in approximating ln(sec(−0.4))by its fourth degree Taylor polynomial at ?=0.

A:

Q: The integration expression + 4)cos(3ln(x) +4)dx must be transformed into using suitable choice of…

A:

Q: Place these trig equations into general form: 1. y = sin (4x + 3π/2) + 2 2. y = cos (3x - 6/7) 3.…

A: According to our guidelines we can answer only three subparts, or first question and rest can be…

Q: iii) E(-1)"+1 cos²(÷) COS n=1

A:

Q: Find the critical points of f (x) = 2 cos 3x + 3 cos 2x in [0, 2π]. Check your answer against a…

A: Given: f(x)=2 cos(3x)+3 cos(2x), 0, 2π

Q: 41-44 Use Theorem 13.5.3 to find dy/dx and check your result using implicit differentiation. 41. x²y…

A:

Q: The integration expression sin(3In(x) + 4)cos(3In(x)+ 4)dx must be transformed into using suitable…

A: topic- indefinite integration

Q: f(x) = cos(T.x)+ sin(27x).

A:

Q: tan 2x – 1 dx. 5 tan 2x + 5 Q5: Determine 1 In |sin 2x + cos 2x| + C 10 A 1 В In |sin x + cos x| +C…

A:

Q: 5. Verify whether the function f(z) Cauchy-Riemann equations or not. sinh 4x cos 4y + i cosh 4x sin…

A:

Q: Show that cos 3x = 3x has a solution in the interval [0, 1]. Hint: Show that f(x) = 3x – cos 3x has…

A: solution:-f(x)=3x-cos3xapplying intermediate value theoremintermediate value theorem states that if…

Q: Prove that sinh−1(x) = In( x+Vx2 +1)

A:

Q: The integration expression sin(3In(x) + 4)cos(3ln(x) + 4)dx must be transformed into using suitable…

A:

Q: Evaluate the integral. sin (3t + 17) dt cos (3t + 17) sin (3t + 17) dt = - 2, cos (3t + 17)

A: Consider the integral

Q: What is the approximation of the value sin (1) obtained by using the fifth-degree Taylor polynomial…

A:

Q: Find the iterative scheme for the root of equation sin x-3x +1=0 by Newton-Raphson method. O a. None…

A:

Q: 1)f sin 4xdx cse(2+3lnx) dx 2) fcos 2xdx 7)f sec (4x)dx 3) fx tan(2x2 +1)dx 8)fx csc| 3- dx 3 dx…

A:

Q: If f(x) = sin(x)e2x, then f"(x) = A) 3sin(x) e2x + 4cos(x) e²*. B) 3sin(x) e2x + 2cos(x) e²x. C)…

A: The given function is: f(x)=sin(x)e2x to find the second derivative f''(x). For that one has to find…

Q: Find the indefinite integral. [ cos 3xar sin33- sin 3r +C 6. O sna(3- sn'ax) sin3 3-sn 3 +C sn3x…

A:

Q: 3. On (-∞, ∞), three functions y₁ (x) = cos 2x, y₂(x) = sin² x, y³(x) = cos² x are linearly…

A: Note: As per the guidelines we are supposed to only one answer because this is not a subparts…

Q: Use Newton's method to find the second and third approximation of a root of 3sin(x)=x starting with…

A: Here 3sin(x)=x∴3sin(x)-x=0Let f(x)=3sin(x)-x ∴f′(x)=3cos(x)-1 x1=2 1st iteration…

Q: Integrate with respect to x: sin(3x) a b 2 cos(4x) cos (2r) (5) f e2x cos² () d 3 cos 3 sin(2a) — е…

A: We have to solve the following integral .

Q: Find Fourier transfarm f x #1= cos aut ut

A: Given the x(t)

Q: The integral of the given function csc x dx is equal to 3cos' x-10sinx cos'x-15sin xcOsx 15sin'x…

A: To evaluate the given integral.

Q: In the integration of (cos x)^4 (sin x)^3 dx, what is the appropriate transformation? * A.) All…

A:

Q: By integration find the Fourier transform of Ax)=2r+1 _if þx|<1_and fx)=0 otherwise.

A: According to our company policy, I am supposed to answer only one question at a time. For the rest…

Q: ( 2 3 2 cos* 3 sin dx O (3/14) cos*7 (2x/3) - (3/10) cos^5 (2x/3) + C O (3/14) sin^7 (2x/3) - (3/10)…

A: Here, we need to find the integral ∫sin323xcos423xdx. So,                ∫sin323xcos423xdxLet…

Q: This is exercise 12 of Section 7.5 page 460. Find the integral sin(2x) dx +C 1+ sin (x)

A:

Q: Find all critical point of the function f(x)= sin^26x+cos6x , 0<x< pi/3

A: Use the graphical approach to determine the critical points for f(x). Plot the curve for f(x).

Q: Give two examples of the situation with the solution clearly and in order Soperties of Bessel's…

A:

Q: The 2nd approximation to the real root of the equation x³ – x² – 1 in the interval [1, 2] using…

A:

Q: Evaluate: f(cos 5x - 2 sin 3x) dx O sin 5x - cos 3x + C Osin 5x - cos 3x + C O sin 5x+cos 3x + C…

A:

Q: Use Cramer's rule to solve for x' and y' in terms of x and y. x = x' cos 0 – y' sin 0 y = x' sin 0 +…

A: Solution is given as below:

Q: 7.2 (A) 1. S sin x dx cos x + C because(-cos x +C) = %3D dx 2. S cos x dx = because sin x 3. S tan x…

A: We need to solve the given integral. This can be done as follows:

Q: [² 11. [(2 sinx+cos.x) dx 9. 13. 15. x¹/3 19. 21. 3 x2/3 - dx 17. [(3 cos x - 2) dx [(5x- 2²/1) dx…

A: Disclaimer:  “Since you have asked multiple questions, we will solve the first question for you. If…

Q: Find the derivative of f(x) = ecos² (3x+1) Of(z) 6 sin(3r+1) cos(3x + 1)ecos² (3+1) O (E) None of…

A:

Q: 2. For the continuous time periodic signal x (t) = 2 + cos(# t) + sin( t) determine the fundamental…

A: Given continuous time periodic signal is x(t)=2+cos2π3t+sin5π4t                            (1) The…

Q: Evaluate the integral. sin (6t + 17) -dt CoS 2 (6t + 17) sin (6t + 17) dt%3D cos 2 (6t + 17)

A:

Q: Use the Definition of a Definite Integral or Theorem 4 from Section 5.2 to find the exact value of…

A:

Q: Compute cos(4x) -∞ (x²+2x+2)' dx.

A:

Q: Approximate cos⁡(−0.3) with a Maclaurin polynomial of degree 2. (Enter either an exact answer or at…

A:

Q: Integrate f Osin-15x+C ○ -sin-¹5x + C 1 dx 1-25x2 - 5 H|K sin ¹5x + C cos ¹5x + C

A: