The graph of g consists of two straight lines and a semicircle. Use it to evaluate each integral. y y = g(x) 10 20 35 10 (a) д(x) dx 30 g(x) dx 10 (b) 35 (c) g(x) dx 20

Q: 3.2.10 Example: By method of contour integration, prove that dx = t /4 (1+ x }

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Q: Find dy/dx by implicit differentiation.   1) x3 + x4y4 + y7 = 5   2) x^2 / x+y = y2 + 7

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Q: Use Version 1 of the Chain Rule to Calculate dy/dx

A: y=5x2+11x20Chain rule:dydx=dydu.dudx

Q: r3 V9-x² »6-x-y dz dy dx in the order dz dx dy 0,

A: Given triple integral is ∫03∫09-x2∫06-x-ydzdydx

Q: Evaluate.cuse C for the Constant of integration). 40 t6x-X dx

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Q: The integral dx Vx² – 4 3 -2

A: To evaluate the given integral

Q: Differentiate the function. y = V 3x2 + 8x + 1 dy dx

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Q: use Separation of Variables to find the general solution. dx/dt= (t + 1)(x2 + 1)

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Q: Determine dy for y=VX2+1 . dx2 alx

A: Obtain the second derivative as follows.

Q: Evaluate the triple integral. 6xz dy dx dz 0.

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Q: Evaluate the double integral : (y³ – 12x) dx dy -

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Q: Evaluate ∫ 2xex dx using integration by parts with u=2x and dv=ex dx. Give only the function as your…

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Q: If f = 5x2y2 - XY2 then find af at (3,1) %3D dx

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Q: Differentiate the function. y=(4x-4)° (3-x)? dy dx

A: Given query is to find the derivative of the expression.

Q: Take a look at the derivative of the integral (4t² – 2t + 7) dt. d - dx -4

A: topic - derivative and integration

Q: Evaluute the integra dx 0 16+49x2

A: Here we have to evaluate I=∫-∞∞dx16+4x2

Q: xy + 8y² = 4 d?y -(y/(x+16y)) dz?

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Q: 4. Use the contour integration to find f G dx. 1 x4+16

A: Answer: π/(16√2)

Q: Let y=5x^2Find the change in y, Δy when x=3 and Δx=0.2Find the differential dy when x=3 and dx=0.2

A: To find the following parts. 1.)find the change in y (∆y), when x=3 and ∆x=0.2. 2.)find the…

Q: 3). S eax cos(mx) dx

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Q: Find aff dy dx² for f(x, y) = exy

A: I have done solution in detail....step by step....go through the solution

Q: Differentiate the function. y= (5x- 1) (1-x°) dy %3D dx

A: Given that the function is      y = (5x-1)2(1-x3)4

Q: Use the change of variables u3 = x2 - 1 toevaluate the integral

A: Given: I=∫13xx2-13dx                       ..1 for evaluating given integral we substitute x2-1=u3…

Q: (y5 – x²e») dx dy -11-3

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Q: b. y = cosh(arctan 3x) C. y = 4a/ cosh a d²y d. for x = 4v2t2 + a, y = a² – t² dx2 %3| -

A: Given functions are  b) y=cosh(arctan3x) c) y=4acosha d) d2ydx2 for x=42t2+a , y=a2-t2

Q: x'dx √√x(1-x)

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Q: Find the solution and the interval of existence for  (1-x2)dy/dx +2y = (1-x)2

A: The objective is to find the solution and existence for  1-x2dydx+2y=1-x2dydx+21-x2y=1-x1+x The…

Q: Solve using the integrating factors by inspection (y²-3-x) dy + ydx =0

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Q: dy Find for dx 3) y = In(vx2 + 1+x) sin¯1x X.

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Q: Obtain the general solution using variation of parameter. (D² + 1)y= cotx

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Q: dy dx=? 3.

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Q: (b) Evaluate f 3æ“ In6x dx using integration by parts.

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Q: Find d2y/dx2 by implicit differentiation: a. x3 + y3 = 1 b. y2 = 1 -2/x.

A: a. Given,

Q: One of the correct. steps to evaluate x²inx. x²Inx dx to yield the correct integral (A dx x2Inx B x³…

A: The given integral,     ∫x2lnx dx

Q: Solve using the integrating factor by inspection  (2x²y - y²x + yx) dx + (3x³ - 4x²y + 3x²) dy = 0…

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Q: Find the dy/dx by implicit differentiation. yvx +1= 4x - 2y 2(x+1) x+1 O Xxww wwxx 2y 2(x+1) x+1 O…

A: Given:  yx+1=4x To Find: To find dydx by using implicit differentiation.

Q: Evaluate ∫12xex dx using integration by parts with u=12x and dv=ex dx. Give only the function as…

A: Here, we are trying to integrate the product of the functions 12x and exTo use the integration by…

Q: Use the Trapezoidal Rule with n = 4 to estimate f, (x³ + 1)dx.

A: We have to estimate ∫-11x3+1dx by using the Trapezoidal rule with n = 4.

Q: 1 .2 2 dx = 0 xe 0- -

A: Given: 12π∫-∞∞xe-x22dx=0   We know that; ∫eax+bdx=eax+ba+C     Note: As per Bartleby guidelines we…

Q: What is the I.F of dy/dx = y - xy^3e^(-2x)?

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Q: The value of the integral 1 2 x²y° dy dx is: 2..3 1

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Q: To integrate x3 ex2 x " 0x we apply integration by parts and in the form u dv, dv is set as:

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Q: Use integration by parts to evaluate: xe2x dx DA. 2e2*(x – 2) + C OB, x²ex² + C OC. -[2x – 1] + C 4…

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Q: What is the I.F of (x^2y^3+2y)dx+(2x-2x^3y^2)dy=0?

A: Find the integrating factor

Q: dy Find in terms of x and y if x In y + yo = 4 ln x. dx

A: Solution is written in below steps.

Q: Differentiate the function. y=[(sx +2x+3) (x-3)]² dy dx II

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Q: Determine the constant of integration of f (x) = S (15z* – 3x²) dæ if ƒ (1) = 4?

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Q: Find t6e eavation of tangent ine of fcx) = X+) at X=2 X-3

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Q: (x+6)dx (x+2)?

A: To evaluate: ∫x+6(x+2)2dx

Q: If f'(x) = x*, what is f(x)? (Use C for the constant of integration.) %3D f(x) = %3D

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