Problem 2 For each of the following, indicate the proper equation for work: Constant Pressure Combustion: W=mJ Pdv Vs Constant Volume Heating: W-mnRT In Isobaric Cooling: W=mp(v2- Adiabatic Expansion: w-P -Bk Y-L

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A: To evaluate the given integral.

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A: First simplify the given function then use chain rule of derivative.

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A: f(x)=cos h-1(x)domain of the function is [1, ∞)for z=cos h-1x+yxz=cos h-11+yx1+yx ≥1yx≥0

Q: Q6/Find the derivative (df/dx) f(x) =+5 e* %3D -4 x-7/3 + 5e* x-7/3 + 5e* O 1, O 2 Fr73 + 6e"

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A: Solution of the problem as follows

Q: tind the first three nonzero terms in the Maclaurin Series of Flx) = tan %3D

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Q: 1 Let f (x,y)=In . Then f „(1, – 1) =...... 3x²+4y3 XX

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Q: 3. The standard fom of the first order lincar differential equation xdy + (2.xy -3y-4x dx =0

A: As we know that; The standard form of the first order linear differential equation is; dydx+Py=Q…

Q: 2 Integrating factors found by inspection.: fr-y+1tr-af²-y²-1ky =0

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Q: х-у If z=x²sinh then дхду 4-

A: Find partial derivatives.

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Q: 3z-2x² -1 (2z–1)®

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Q: 1. Find the domain and level curves for each of the following. (a) z = 1+x? + y3 (b) z = Va? – y - 3…

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Q: By substituting y=xv, solve the given differential equation, (2xy+ x²) dy = 3y² + 2xy with dx the…

A: The given DE is: 2xy+x2dydx=3y2+2xy⇒x22yx+1dydx=3y2+2xy⇒2yx+1dydx=3yx2+2yx⇒dydx=3yx2+2yx2yx+1

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

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Q: Consider the ellipse with the given characteristics. foci: (0, 0), (0, 10); major axis of length 18

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Q: xdx S- can be solved by either algebraic subsitution or integrataion by parts. x-1 А) True B) False

A: We know that algebraic substitution is method in this replace the veriable of integration by a…

Q: 4. Determine the equation of the tangent line to y = x²sin2x, at x = - R

A: Follow the procedure given below.

Q: Evaluate the definite integral by choosing the appropriate substitution. You must show your work. 8…

A: Basic definite integration problem

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

Q: dr

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Q: Find the derivative of the following functions and simply it whenever possible. 6. y = ln(ln sec x)

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Q: cosßdß 2+3sinß

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Q: 2 dt t² +2t +3 18. Evaluate 8 dz z² +8z+ 25 20. Evaluate o

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A: I have provided this answer with full description in step-2.

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Q: If z=x²sinh then дхду O A. (-x³– 3x²y+2xy² – 32x) / 16+x²- 2xy + y² (16+x²-2xy + y²) ² O B. (x³–…

A: Given  z = x2 sinh-1x-y4 We have to find  ∂2z∂x∂y.

Q: 2. Computing Derivatives; Compute each derivative using the derivative rules: d (a) (cos-(1+ 2*) +…

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A: Detailed explanation is attached.

Q: i sin(In(-32)) = cos(In(-32²). True or False: dx True O False

A: Topic = Derivative FALSE