(1) Obtain the complex Fourier series coefficients for f(x)=x for-n

Q: What is y' of y = sin¹ (cos x)? O A. y' = ATHE sin + 1-cos² 1 O B. y' = 1 OC. y'= sin z 1-cos² z OD.…

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Q: Evaluate 1 70 sin° (f (x)) cos*(f (x))g(x) dx COS where g'(x) = r for all x with g(0) = T , • f'(x)…

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Q: cos x a Given that y = show that y' %3| 1 + sin x (1 + sin x)?" b Hence explain why the function 1…

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Q: 3/2 x+3/2 x² - 2 Show that dx = In 3.

A: Since there are multiple questions posted, we will answer the first question posted (4). If you want…

Q: S 1 dx = (x² + 1)(1 – sec(tan-1 x)) Select one: а. 1 -x + (sin(cos-1x)) b. 1 -tan(cot-1x) +…

A: Hence option (d) is correct .

Q: 7/4 2 sec(6x)dx sin(r In(x)) 13x 1

A: (b)

Q: Suppose (=/3) = 3 and f '(m/3) = -7, and let g(x) = f(x) sinx and h(x) = (cos x)/(x). Find the…

A: So, Again, if , Then

Q: Solve the D. E. to the I. V. P. sinx(e- + 1)x' – cosx = 1, y(-) = 0 (1 + e") (1 – cos x) = 2 O (1 +…

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Q: Q1: Find dy/dx for the following functions (solve four only):-

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Q: find y'. (show all the steps please) cos(xy) = x-y^2

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Q: 2 Find the second derivative of y = 1½ cos² x. Oy" = COS x 2 y" = COS X sin² x cos² - Oy" = sin² x =…

A: Q.Consider, y=21​cos2x Differentiate with respect to x. y′=21​dxd​(cos2x) Use formula:…

Q: In estimating cos(3x)dx using Trapezoidal and Simpson's rule with n = 4, we can estimate the error…

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Q: Read each of the two statements carefully. Choose A(if both statements are true), B(if the 1st…

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Q: | 1' cos(T +1) dr. COS

A: using the integration by parts

Q: Simplify (if necessary) then 2 Compute: y" +Éy' for a2 y(z) = rar (zx+ cosx')] [6(cosh2x- sinh2x)] d…

A: given yz=∂2∂x∂zz2x+cosx96cosh2x-6sinh2x36cos2πxddx3x2 claim- if necessary simplify then compute the…

Q: Suppose f(pi/3) = 5 and f'(pi/3) = -7, and let g(x) = f(x

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Q: - Find the extreme value/s of f(x) = 4 sin² x cos 2x on (37 3π 5π 22

A: This is a problem related to maxima and minima of the function. Based on the general formula and…

Q: Evaluate: 4S d sin(t?)dt dx x 3x²sin(x“) – sin(x²) b. 2x°cos(x°) – 2xcos(x²) a. 3x²cos(x^) – cos(x²)…

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Q: Use the appropriate rules to differentiate two of the following: (a) y = e* cos4x (b) y= (4x² +8x)*…

A: We need to differentiate the given functions. this can be done as follows:

Q: Find f if f" (x) = 2 + cos(x), f(0) = -8, f(T/2) = 8. *(x) :

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Q: 7- I = [sec(2x) tan(2.x)dx cos(2x) 8- I = dx 4-sin (2x) csc (In(x)) 9. I: dx

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Q: Find f. f(0) = f"(0) = sin(0) + cos(8), cos(8), f(0) = 1, f '(0) = 3

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Q: (#5) ſ cos³ (x)sin*(x)dx =

A: Given the function,

Q: Find f. f"(8) = sin(0) + cos(8), F(0) = 5, f(0) = 4 F(8) -sin(0) – cos(0) + 5x + 6

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Q: 7 (1 + sin² x) = e 2" sin 2.x, y(0) = 1 X 7) dx

A: This equation solve by separation variable

Q: Find f. f "(0) = sin 0 + cos 0, f(0) = 1, f'(0) = 3

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Q: (1 point) Approximate cos(4.6) using a quadratic approximat First note that cos(4.6) cos(3/2). Let…

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Q: y=(b+x²)* +(1+x³)*(/3x² +x – c)cos²(4x) y' =?

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Q: 1/2[22500/tan(π/6)]

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Q: Given f''(T) 9 sin(3r) and f'(0) 6 and f(0) = 3. Find f 2.

A: Given f"(x)=-9sin(3x) and f'(0)=-6 and f(0)=3

Q: Solve the D. E. to the I. V. P. sinx(e¬ + 1)x' – cosx = 1, y(곡) = 0 - O (1 + e') (1 + cos x) = -1 O…

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Q: Which of the following functions are of exponential order? 1. e³t^2 2.4t³-9t+11 3. Sinh(t2)…

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Q: Step 2 Now, . 유 sin (플)dr cos h(1 Lx)–I %3D =L (cos h (11x) – 1)dr a cos h (11x)dx – L" Idx sin h…

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Q: 1- 2- If x=y√√1-y², find Find y' for y=cos(sin²x) dy dx

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Q: Find f. f"(e) = sin(e) + cos(e), f(0) = 5, f(0) = 4

A: f''(θ)=sin(θ)+cos(θ)Integrate with respect to θf'(θ)=∫sin(θ)+cos(θ) dθ f'(θ) =-cos(θ)+sin(θ)+C1Again…