Problem 7.2. Using translation and scaling invariance only and Prob- lem 8.1 (linear substitution) and 2nd FTC, calculate the following in- tegrals: (1) So sin(3r + 1)d.x. (2) S cos(3x + 1)dx. (3) S" (3x + 1)51 dx.

Q: dx Problem 13. (10) Evaluate by making the substitution x = tan u; remember the (x² + 1)2. limits.

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Q: Question 21 If y- 2x+6x and - 6, find dy when x 5. dt Select the correct answer. none of these 928…

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Q: Problem 2: ka3 Find dy/dx at x1 from the following table of values 2. 3 4 27 64

A: We will answer the first question as we don't answer multiple questions at a time. Please resubmit…

Q: Problem 16. (a) Calculate the following antiderivatives: //=/ dx = (b) / -55 (c) / 2e" dx = [ -5 sin…

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Q: Solve the following problems. 2. 2x°cos 5y+ x tan5y dy=0

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Q: Problem 2. Show that J. 3 sin x -dx= (1 2 x(x² +1) If you want to use Jordan's Lemma, justify the…

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Q: Problem #6: Find the equation of the line tangent to f(x)= cos² x- sin? 1 at x = -. - 5x 6.

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Q: Problem 6 (1-cos2x)+2cos²x S V2x + 1 x² dx

A: Solved below

Q: PROBLEM 1 : J sin'y cos y dy ROBLEM 2 : S cos*x sinx dx os==dy y-1 PROBLEM 3: S sin- ROBLEM 3 : 3 3

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Q: Evaluate the integrals in Exercises

A: Question 7 - Let the given integral be y - y = ∫lnx-5x-5dx       ............(1)Let,t = lnx-5…

Q: Problem 2: Find an ODE of the form + P(x)y = Q(x); y(0) = a (i.e., find P(x), Q(x) and a) whose dx…

A: The solution to the ODE is: y=2sinx-cosx+2e-x......(1) At x = 0, y = a, so…

Q: Problem 23 What is the length of the curve ln(sec(x)) from x=0 to x=1.3?

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Q: Repeat Problem 109 for g(x) = cos2 x.

A: g(x) = cos2x

Q: Problem 7.4. A particle moves along the x-axis such that the velocity is given by v(t) = 3t + cos(t)…

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Q: Problem 3. Show that the function cos(n²x) 2n f(x) = Σ n=1 is differentiable on [0, 1] and f'(x) is…

A: Given :  f(x) = ∑n=1∞cosn2x2n To show :  f(x) is differentiable on 0, 1 and f'(x) is continuous on…

Q: 3. In problems 1-8 find the least order DE which has the general function as its general solution: ,…

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Q: I Problem 1. Find both the signed area and the area between each of the curve y = x² - 6x +5 and the…

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Q: In Problems 1 through 6, express the solution of the given ini- tial value problem as a sum of two…

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Q: Problem 3. Consider the function 1 F.(s) = %3D 1+(-js)2n 1. Find the poles of F(s). Is F(s) stable…

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Q: Problem 11 Find the integral.  ∫e^(4x) sin(5x)dx=_________________

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Q: Problem 3. Calculate all four second-order partial derivatives and check that fru = fur. Assume the…

A: Given:          f(x,y) = 3sin(6x)cos(2y)          fxy = fyx       fx   = ∂/∂x( 3sin(6x)cos(2y)…

Q: snip

A: Given,f(x)=sinx,g(x)=cosx To find: (f+g)(30o) Solution: f(x)=sinx,g(x)=cosx…

Q: Problem 2. Consider the following composition: f(x) = 3x² + 2, x(s) = sin(s),s(v) = In[3v²],v(t) =…

A: Explanation of the answer is as follows

Q: Problem #6: Find the slope of the line tangent tof x =cos² x- sin? at 1 5x Solution:

A: We have to find slope

Q: In each of Problems 13 through 18 determine a suitable form for Y (t) if the method of unde-…

A: The given differential equation is y'''-2y''+y' = t3+2et. The characteristic polynomial can be…

Q: PROBLEM. dz dz and dy 1. Suppose z is a function of x and y, and tan Vy² + x² = z®e©y. Solve for %3D

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Q: Problem [6 - 8] Use Integration by Parts to verify the specified formulas: 6. fx cos-(2x)dx = x…

A: Solution is given below:

Q: Problem 2. Consider the following sequence of functions fn (x) = r" sin(nr), r€ [0,1/2], n =…

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Q: In Problems 1 through 6, express the solution of the given ini- tial value problem as a sum of two…

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Q: Problem 5 Evaluate the definite integral.  ∫sin^2(6x)cos^2(6x)dx=__________________  (upper limit=7,…

A: Evaluate the integral

Q: Problem 8.6. 1. Let X ~ xỉ. Show that its moment generating function is given by 1 M1(t) = V1- 1 –…

A: Problem can be solved using concept of moment generating function and gamma function.

Q: Problem 8. Let F(x, y, 2) = (2x2 + sin(y), a cos(y), x²) %3D |(8A) Show that F is conservative. (8B)…

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Q: Problem 1. Let X ~ Gamma(a = 2, 0 = 2). Compute: (1) VaRo.975(X) (2) ex(9.488) (2) TL 1 TVeD (Y)

A: From the given information, X~Gamma(α=2, θ=2) fx=122Γ2x2-1e-x2, x>0      =14xe-x2, x>0 1.…

Q: Problem 1 Apply trapezoidal and Simpson's rules to the integral 1 1-x dx continually halving the…

A: We have f(x) = y = (1-x2)1/2, using this, we can form the table for f(x) with the corresponding…

Q: Problem 13.1. Calculate the follo gration by parts: (1) Sa sin(3r +1) dx. (2) Sa'e(3r+1 dr. (3) ſ…

A: Since You have posted multiple subparts questions.  As per our guidelines we will do the first 3…

Q: The solution of the following Bernoulli's equation xy' + 2y = x¹(cos x) y² is

A: The correct answer is not given in options.The solution with the correct answer is given as

Q: Problem 1  Verify that  (1/((x^2)-1))=(1/2)[(1/(x-1))-(1/(1/(x+1)) And use this equation to evaluate…

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Q: Problem 1 Find the derivative for the following. (a) g(x) = Sï 7 dt (b) g(x) = Sing V1+t²dt (c) f(x)…

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Q: Problem 8.6. Find the following antiderivatives: r+1 1) S (플프2+피+27)" 2) f cos (x)dx cos(I) dr 3) J…

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Q: Problem VII: Evaluate ye"dx +xe"dywhere C is the portion of the curve y = x' - x² +1 from (0, 1) to…

A: Given - ∫Cyexydx + xexydy  where C is the portion of the curve y = x3 - x2 + 1 from 0, 1 to 1, 1 To…

Q: Problem 7. Let f(x) = xe". Compute y', y" , y'" , y(4), y any integer n > 1? Problem 8. Find the…

A: NOTE : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: Problem 1. What is the distance travelled by a point during the time t, if it moves in X- Y plane…

A: Given that x=asinωt and y=a(1-cosωt) are relative to each other. We need to find the distance…

Q: Pls help ASAP.

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Q: Solve the tollowing problems. 2. 2x°cos 5y+ x tan5y dy=0

A: Introduction: Separation of variables (also known as the Fourier method) is one of several methods…

Q: Problem 5. Find the derivative of each of the following: d {cos(2z + 3i)}², 1) dz d {(2)[tan"'(In…

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Q: Problema 3. Si R= [0, 7] x [0, 7], hallar: | cos(2r)- cos(y)ldædy

A: The given data is: ∫∫Rcos2x-cosydxdy

Q: Problem 1. Calculate the approximate area under the curve of: 10 |-0.01646x +0.16253x² +0.07881x…

A: Given integral is ∫110 -0.01646 x3+0.16253 x2 +0.07881 x +4.85467 dx Take  ∫110 -0.01646 x3+0.16253…

Q: Find the solution to the following Bernoulli's equations. 1. y3 sec x dx - y tan x dx = dy

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Q: Part 3 of 3 This gives us 글|10 cos(0) + 20 cos(금) + 20 cos() + 20 cos( cos() cos()] T4 + 10 8.957589…

A: Given the integral is, I=∫0110cosx2dx The above function is to be calculate by 4 trapezoids as,…