Let f(x, y, z) = ln(x² + z) + y²e"z – cos(2yz). Find fzya- CoS %3D

Q: Find the antiderivative of 5sin x In5 cos x dx 5coS x + C 5sin x In 5 + C O sin x + C In 5 5sin x +…

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Q: |-2 Evaluate the triple integral ²³ cos (y²) dz dx dy.

A: Here we have to perform triple integration

Q: * t/3 Evaluate the integral S'(y cos x – 3) dydx. S x -

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Q: Determine the general solution on the given D.E. by using Separable Method: sin a sin y de + cos a…

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Q: TC 16. Evaluate the definite integral cos2 (4t –) dt

A: 16. Now,

Q: Q3/ Evaluate the integral: TT ° cos(x²)dx dy

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: [-4ycos(x)+4sin(x)cos(x) +sec°(x)]dx +[4y=4sin(x)]dy = 0, y= TC = 0 2y-4ysin(x)-cos(2x)+ tan(x)= 1…

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Q: Q3. (30pt) Calculate the integral 2x³ – 4x + 1 - (1– cos x) dx 1+x? a) for n= 10 according Simpson…

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Q: Find the most general antiderivative of the function g(x) 3x2 -e + coS I | O 6x-ex-sin(x)+C O…

A: The given function,  g(x)=3x2-ex+cosx  .................................(1)

Q: Recall that 1, x >0 d (]xl) dx —1, х<0 x < d Use this result and the chain rule to find (sinx|) for…

A: Here, recall that  -π,-π2 is 3rd quadrant, where sin is -ve-π2,0 is 4th quadrant, where sin is…

Q: 6) Use integration by parts to evaluate the following a) S Vx In x dx b) S e2x cos3x dx c) S“ x³ cos…

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Q: 3. Find the linear approximation to g(z) = cos(z + 1) at z = 0. Use the linear approximation to…

A: The formula to find the linear approximation L(z) of a function fz at point z=z0 is: Lz=fz0+f'z0z-z0…

Q: Solve the problem. Integrate f(x, y) = sin(x2 + y2) over the region 0<x2 +y2< 100. O T(1 - cos 100)…

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Q: (sec2 x + csc2 x)cos2 x dx

A: Given: I=∫sec2x+csc2xcos2xdx   Use the trigonometric identity; 1). sinx=1cscx 2). cosx=1secx And…

Q: (e) f(x) = sin(e*) + eco«(a) (f) f(x) = cos(x) In(5x) (x) S(z2) = ()" %3D - 1

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Q: Use Secant method to to approximate the solution of f(r) = z+ cos z =0 accurate to within 10-3,…

A: The secant method is used to calculate the root of the function. The formula for the secant method…

Q: 4 dx Vx(1 + x) roper for two reasons: The interval [0, co) is infinite and the integrand h 4 4 dx =…

A: Here we use substitution so simplify the integration.

Q: If In y = 3 sinh x show that dy (a) (1+r2)()² = 9y², dx (b) (1+ x²)- dy da? dy +x- – 9y = 0. da…

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Q: 1. Evaluate the iterated integral: r12 Jo o cos(2) dy dx. -

A: To find ∫π2π∫0x21xcosyxdydx: First solve ∫0x21xcosyxdy: Let u=yx  dudy=1xdy=xdu…

Q: Pind the derivativa otthe Pollowing の3=2 Sin'Csx) In coshラX 3 =\nx (3) Xsin 4y=Jtan YX

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Q: Find a differential operator that annihilates the given function 1. y= 4e* +3e¯* 2. y = 2e cos 3.x…

A: According to our answering guidelines we can only answer 3 subparts at a time, rest you can repost…

Q: -) A) Find by using chain rule if f = ( , u = -1,x=-1 dx u+1 B) Evaluate the following integral:…

A: This question is based on chain rule differentiation and indefinite integral.

Q: 1. Evaluate the integral 2 1-2 8x cos y dy dr y - 4 by reversing the order of integration.

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Q: Show that the process X(t) = A cos At + B sin At (where A and B are RVs) is wide-sense stationary,…

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Q: 2) Let 1 = f* cos y3 dydx. By reversing the order of integration of I, we get a. 1 = ²₂x cos y³ dx…

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Q: Find the temperature u(x, t) in a rod of length L, if the initial temperature is f (x) = 100 sin 6nx…

A: Given function is, fx=100sin6πx at x=0 and x=L Now, we know that, ∂2t∂x2+qgk=1α·∂t∂z....(1)

Q: Let z = tan-1(E) – In(cos y), where r = T- u and y = uv. Use multivariate chain rule to find the…

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Q: Use an integrating factor to solve the IVP y'+ytan x = cos x, with IC (x, , Yo) = (0,7), %3D and…

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Q: Find and show the work for 2 (x+3)(3x+2) dx. (a) (b) SF (sin(2x) – cos x) dx.

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Q: Let f(x, y, z) = ln(x² + z) + y²e#z – cos(2yz). Find fzya.

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Q: 3. The integration of x e* with respect to x is: A. e2x. В. 2хе* С. 2

A: To integrate  xex2 with respect to x: ∫ xex2dx Apply u-substitution: u=x2 Differentiate both sides:…

Q: •1 r1 Evaluate the double integral / /. cos(y*) Vy³dydx

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Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

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Q: Find the general antiderivative of f(x) = 2 cos (x) – 7 sin (x) and check the answer by…

A: For a function g(x) if f(x) is the derivative of the function such that ; d(g(x))dx=f(x) Then;…

Q: Evaluate the double integral. eln 3 3 7 dx dy In x ey In 3 3 7 dx dy = (Type an exact answer in…

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Q: on 1. Complete the following computation a' In(8x)dx via integration by parts f(x) = In(8x) and…

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Q: A) If w = 2 y et* – In z where x = In(t² + 1), | dw y = tan-1 3t and z= e3t. Find by Chain Rule dt

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Q: 1. Find an antiderivative of f(x) = 16–x². Then, use The Fundamental Theorem of Calculus %3D 4 to…

A: Given : fx = 16-x2

Q: Find the value of the improper integral or state that it is divergent. (If it is divergent, enter…

A: We will calculate the definite integral using basic definite integral properties and if we get an…

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

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Q: Let C be a positively oriented smooth curve with interior D. A function f : R² → R is called…

A: Given: ∫C∂f∂ydx-∂f∂xdy ∂2f∂x2+∂2f∂y2=0

Q: II cos(s5) dt ds

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Q: 1. y = Ax² + Bex 2. y = C₁ ex cos3x + C₂ ex sin3x 3. y C₁e* + C₂e²x + x 4. Iny = C₁e* + С₂е¯* 5. x =…

A: As you have asked multiple questions so that I have answered first question as per the guidelines.

Q: Compute the general antiderivative S a"-1 cos(x")dx COS where n > 1 is an integer greater than 1.

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Q: Show that the p.d.f. of Z is given by g1(r) = e-1(+A)cosh(vAx), x > 0, where cosh(2) = }(e² +e=*) is…

A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

Q: A:= {(x, y) € R² :1< log(x) < 2}. = {(x, y, z) E R³: sin(xy² + «/2) · cos(z) = 1} . (a) Decide…

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Q: 3. Find the general solution of xy' = x – y + xytanx a. xycos x = xsin x + cos x +C b. ycos x = xsin…

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Q: Find the Wronskian for y, = sin 3x , and y2 = cos 3x.

A: The Wronskian, W, of two functions, f and g is calculated as follows. W=fgf'g' , where, f' , g'are…

Q: 3. Let V = eP cos(qr), with p = x In(xyz), q = z cos(Ty) and r = 2 tan-(y). %3D By using the chain…

A: Solve the given problem.

Q: 1. Integrate by parts and evaluate x cOS x dx 0, а. b. In(x²) dx 1 In x dx x5 С.

A: By using Integration by part  ∫udv=uv−∫vdu