3 1 1 1 dx in terms of k. 6. If dy k, find 1+y 1+9x2 0 Sin (p tos - l tan + C

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A: Solution

Q: 1. f(x) = In 5x 2. у %3D 103х Final Answer: Final Answer: 3. y = sin(e3*) 4. y = cos 2x (e*²-1)…

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Q: 1.Given x=3( θ-sin θ) and   y=3( 1-cos θ) a. Find dy/dx b. Find d/dx2

A: Given: Given x=3( θ-sin θ) and   y=3( 1-cos θ)  a. Find dy/dx  b. Find d/dx2

Q: d² dx dx 3. di² +2 +5x = sin 21, given that when t = 0, x = 3 and dt dt 53 [ 55 Ans. e 17 cos 2t + -…

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Q: 1 f(t) dt = ln(x) cos(x) + /. e* f(t) dt, find f(x). You may find FTC 1 useful. n(3) Given sin(3)

A: The solution are next step

Q: 4 T 40 sin(3x)dx None of them -0.532 -0.253 0.253 -0.235 0.0235 -0.325

A: Solve the definite integral

Q: TL 2 Evaluate the integral: sin(3x)cos(3x)dx 3 1 A B C D H|m 3 16 1 3 16

A: To evaluate the integral. Option c is correct.

Q: 3 T 3. Find the exact value of sin 8. 1 + cos 0 - cos e 1 = + cos = ± sin cos O tan 1 + cos 0

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Q: The approximation of I = S cos (x² + 5) dx using simple Simpson's rule is: 0.54869 "-0.93669 This…

A: We have to solve by Using Simpsons 1/3 rule .

Q: 3. S cos ædæ from a = 0 to b = 5

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Q: (b) S¤(tan? #)dx (c) S cos(2t)e'dt (d*) S(arccos x)²dx (e*) S (1+ 3x)2 dx Hint: Check for a similar…

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Q: 1/2 Evaluate I = dx correct to 3 decimal places using Romberg's method. sin x %3D

A: Here A is the sum of the first and last value  B is the sum of other values

Q: 13 9 2 cos dx dy dz =| 0 0 3y (Туре an exact answer.)

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Q: dy for 2xy = dr 4 cos(x) – y?." as Problem 18: A student answers a homework question "Find follows.…

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Q: The approximation of /= cos(x³ + 5) dx using composite Simpson's rule with n=3 is: 3.25498 0.01259 O…

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Q: 6. (a) Find a function u(x, y) that is harmonic in R2 and that equals f(0) = sin(30) + cos(40) on…

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Q: 2a's at L{sinh at sin at} = (s* +4a*)

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Q: Find dy/dx for each of the following. Do not simplify your answers. (d) y = (In x)tan æ (x + 4)4 (4x…

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Q: 1 E valuate [ (x' + cos(3x)) dx sin (3x) a) b)

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Q: 5. x = cos 2t, y = sin 2t, 0 <t< T

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Q: 2 4x (a) S rdr, (b) § sin 0 d0, Cos2/3 g do, (c) St(2t – 5)" dt.

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Q: Given (1+ 3x sin y) dx – x² cos y dy = 0 with y(1) = 0. Using Euler method with h=0.05, y(1.15) =…

A: Euler's method uses the formula: y1=y0+hf(x0,y0) to perform the iterations.

Q: Given 5y + cos(3y) = x³ Implicitly find dx Select one: 3x Sy²+sin 3y a. 3x O b. 5y²-sin 3y C.…

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Q: 1. (a) Find L{t*e*t – e' cos v7t} (b) Find L{sin 2t sin 5t}. [ Recall sin Asin B = (cos(A – B) –…

A: Since you have asked multiple questions, we will solve the first two questions for you. If you want…

Q: 4. If f(t) = 3 sin(4t + 0.12) – 2 cos(3t – 0.72) determine f'(t) when t 1 5. Evaluate when x 1,…

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Q: 6. Find * : y- + 5)ao TK, (b) y = Sin 5x I+cos 5x dx

A: Solving the problem by finding the derivative.

Q: 1 1² +49 When solving O a) I = [sen (0) de Ob) I=tan(0)de O c) I = cos(0)de I= O d) I-sec(0)de I=…

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Q: 41. * + 4x + 5x = 8 sin t ; when t = 0, x = 0, x = 0. Note that i = is a common notation when the…

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Q: i1. L'[s/(s² +a)*]= (1/2a) t sin at 12, L' [1/(s² + a?)² = (1/2a) (sin at – at cos at) %3D

A: Introduction: The convolution is very significant in calculatig inverse Laplace transformation.…

Q: 2n 37 So² S67 (x sin(y) – y cos(x)) dxdy = %3D

A: The given question can be solved as shown in step 2.

Q: The integral cos(x − 3) dx is transformed into f, g(t)dt by applying an appropriate change of…

A: Solution :-

Q: Evaluate k sin(kx – T) dx where y and k are independent of æ, and y is given by the solution to the…

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Q: A particle moves along the x-axis with velocity given by v(t) = 8 cos (4t) for time t > 0. If the…

A: Given, A particle moves along x-axis with velocity v(t)=8cos(4t), t≥0. Particle at position x=-6 at…

Q: (3+ )t Given yo e (3-)t Yo= e (as above ) with the form e cos (at) aned ert sin (Bt) that de not…

A: See the attachment

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…

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Q: 1. S" cos? (2t) dt u-sub = 2. S sin5 0 cos* 0 d0 power on sin is 'odd'

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Q: 2π π14 cosφ SSS p' sinødp døde 0 0 0

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Q: sốn ² sin () cos() sin() dx (Consider initially the first 2 terms)

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Q: dy 4)y = sin-1) veriliyor. i bulunuz ve sadeleştiriniz. dx

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Q: 1. (a) Find sin 6x+ cos 4x dx. (b) Evaluate dx. Hence, solve dx. (e' +2) (e'+2)

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Q: 4 T/2 a, = f(x)cos(n@,rkdr = "jxcos dx %3D sin 4 cos 2 2

A: Okay I am explaining the marked step.

Q: 1. (a) Find L {t*e#t – e' cos v7t} (b) Find L{sin 2t sin 5t}. [ Recall sin A sin B = }{cos(A – B) –…

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Q: 1. Evaluate 9/ COS x (a) (1 – x)e dx (b) ,"™ dx p) A-2 sin r -

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Q: 9 3 12 6 cos (x) SSS dx dy dz =| 0 0 4y (Type an exact answer.)

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Q: 7. 3cos (@t – a), where o and a are constants 8. Show that L(cos 23t – sin 2 3t) = s²+36

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