7. Set f(x) (a) (b) (c) (d) = 2 +4 8 cos 2x, 2sin2, + e-8/2 s² + 4 S s² +4 8 8² +4 (e) None of the above. +e-8/2 +e-8/2 -e-8/2 S 8 0≤x≤π/2 * Σπ/2 [s² +4 28 [s² +4 2 - 2s $² +1. 2s s² + 2 s² + 1. 28 s² + 1. L[f(x)] =

Q: le“ + 4x° + 7 cos x + 2)dx O 4eª + x*+7 cos x + 2x + c r4 x* + cos x + 2+c - O 4e" + x* – 7 sin x +…

A:

Q: 11. Evaluate 1 (a) √x (x² +1)³dx, (b) fdx (c) fda (d) fx x+2 ev dx √x²+4x IT'

A:

Q: The f sin 2x cos 2x dx is 1+3 cos 4x 1 sin²4x + C 24 1 In|1 + 3 cos 4x| + C 12 {A} {B} {C} - In|1 +…

A: To find the value of the given integral ∫sin2xcos2x1+3cos4xdx using substitution

Q: Evaluate L{u(tπ/2) cos 2(t- π/2)} Option 1 Option 3 se πs/2 8² 2 3e-s $²9 O Option 2 O Option 4 3es…

A: Here we have to find the laplace transformation of the given function.

Q: If y = (4r² + 1)* (1 – 2*²then A y' = -4x (4x² + 1)² (1 – æ*) (æ + 6) B None of the given choices O…

A:

Q: Find L[e2t tsin(2t) + et+1 + et cos 2t] A)+ 28-4 s+2 (4-1)2 +4)a (+2)a +4 +2 B) 4-4 1-2 1-2 (-1)2…

A: Use the formulas below to calculate the Laplace transform.

Q: 6. Setting æ = cos 0 show that T.(e) = [(- + ivI- =')" + (* - ivī- =')"] n where i = V=1.

A: This immediately follows as a consequence of De Moivres formula which states that e^(it)=cos t + i…

Q: Deduce that if (b) Let a 2 cos 2 and ß = 2 cos 4. Show that a = @ +w4 and B=w² +0³. Find a quadratic…

A:

Q: 3.) If g(x) = cos 2x ,Find g ().g ), g(-x), g(n – x), g (n + x),g(x -)

A:

Q: = )* - a) Va' + 1) zVx +1 +C b) Va' + 1) - 2V +1 + C Q3: S dx%3D c) V + 1

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 2 1.f(3x²+5) cos 2xdx 0

A: We need to perform integral. NOTE - As per Bartleby guidelines we can solve one question from…

Q: Compute[x² sin(2x)dx. A.- x² cos(2x)+ xsin(2x)+ cos(2x)+C 1 1 B. — — x² cos(2x)+ —…

A:

Q: 2. f(x) is the function whose graph consists of the two bold line segments shown in Fig. 7. (-7, 0)…

A: What is Fourier Series: A Fourier series is a total that sums the sine and cosine waves to depict a…

Q: If S", f(x) cos(mx)dæ = } g ar cos(n²a) f(x) = Ln=1 nt +1 then m =

A:

Q: 4. Suppose the following functions are a general solution of: y(4) + azy" + azy" + a13 + a0y = 0…

A: The differential equation is y(4) + a3y''' + a2y'' + a1y' + a0y = 0 We have to find a0, a1, a2 and…

Q: (4e® + 4x° + 8 cos x)dx 3 O 4e" + x4 + 8 cos x + c et – x4 + cos x + c et + x4 – 8 sin x + c O 4e" +…

A:

Q: | (5e" + 5x4 + 6 sin æ)dæ %3D e – x + cos x + c x° + cos + c 5e" + x + 6 cos x + c et + x5 + 6 cos x…

A:

Q: (a) Let f(x) = cos(3x – 2). Find f"(x). (39) %3D (b) Let g(x) = 2***. Find g (153) (x). %3D

A: Topic = Derivative

Q: Suppose f(t)dt = 2 + x' + 3x°- cos(x'). Find f(x) for x > 0. %3D O f(x) = 1 + 6x² + sin(x²) O f(x) =…

A:

Q: | (6e"+6x° +4 cos x + 2)dx = %3D 6e + x° + 4 cos x + 2x + c O e – x° + cos x + 2 + c 6 O e + x° 4…

A:

Q: Show that in the interval (0,1) COS TTX = ∞ TT n=1 n 4n²-11 -sin 2nπx

A:

Q: Tx/2+sin(ix) f(x) = V2r then = (x).

A:

Q: (3e² + 5æª + 6 cos a + 2)dx : 3e? + x + 6 cos a + 2x + c 3e + a + 6 sin a + 2x + c et - x5 + cos z +…

A: Given problem:- ∫ (3ex+5x4+6cos(x) +2) dx

Q: A. (4,00) Suppose f(x)=√4x and g(x)=3x² + 3x-2. Then the domain of f(g(x)) is B. [-4,0) U (0.) C.…

A: As per guideline i can solve only first question

Q: (4e" + 8x7 – 7 sin r)dx: O 4e" – x8 +7 cos x + c O 4e" + x8+7 cos x + c O 4e* + x* – 7 cos x + c O…

A: Explanation of the answer is as follows

Q: (D³ – D²)y = cos2t; y a. y = C, + C,t+ Cze +cos2t-sin2t 10 20 b. y = C, + Czt + Cze-2* cos2t + 10 1…

A: We have to find the general solution of the given  differential equation D3-D2y=cos2t .

Q: Evaluate f 2ema cos (nx) dx 2ema [n cos (nx) a. m2+n? m sin (nx)] + C b. 2emz [m cos (пa) n sin…

A:

Q: If z = x2 – y2 and x t cos 2r and y = r sin t, then %3D a2z is ar2 (A) 2 cos (2r) + 2r? cos?(t) –…

A:

Q: 5. Find L{f(t)} a. f(t) = sin?(t) + t b. f(t) = n² – 8e¬2t + (et + 1)² | c. f(t) = F, sin yt -cos…

A: As per our limit we can solve only first three subdivisions if you want the answer for other…

Q: |(4e" + 8a7 – 7 sin æ)dæ =. O 4e – x8+7 cos x + c O 4e* + x8 + 7 cos x +c O 4e* + x8 – 7 cos x + c -…

A:

Q: (c) L-¹ 2s 14 { (8+3)(8 + + +28+5) 4e-3s -1 s² (s+4)) (d) L-¹ {

A: As per the policy of bartleby the provisions is to solve only one question at a time  but here  I am…

Q: x 16. Evaluate sin dx. f x +C O O- 1 3 cos³x 1 3 cos³x 1 2 cos²x 1 O- + C +C + C 2 cos²x ONone of…

A: we have to slove above integrate

Q: -1 L-1 [wcose+ssine` s²+w² a. sin (wt + 0) b. sin (t + 0) c. cos (wt + 0) d. cos (t + 0) 2}, w & 0…

A:

Q: | (5e" + 5a* + 9cos r+ 2)dr O e* - a5 + cos a + 2 + c O 5e" + a -9 sin a + 2+ c O e +a5 - 9 sin z +…

A: Here we have to evaluate I=∫5ex+5x4+9cosx+2dx

Q: 3x-1 a) The function y=- has a horizontal asymptote at y = 3. x+2 b) cos x cos 4x-sin.xsin 4x=…

A: We have to decide whether the given  statements are true or false.