9) (15 points) The internal energy U of a gas can be expressed in the form U=f(p,V,T) with variables defined by: p is the pressure, V is the volume, and T is the temperature. For an ideal gas, PV = nRT where the number of moles n and R (gas-specific) are constants. a) (3 points) Write the differential form du for the internal energy. b) (5 points) Assuming the volume V is held constant, find an expression for the heat capacity cv where c₁ = au. др

Q: 4) Find the mean and rms value of the voltage v given by the equation V=45sin(wt)

A:

Q: 1. a) Copy and complete the table below: Original Function First derivative Second Derivative f(t)=…

A: Original Functionf(t)=5t−3−5e0=5t3−5f(z)=ln100h(p)=−2e1−pFirst Derivative…

Q: 8. y = (cos 3x)V

A:

Q: Question 20 Find the derivative: x²(x² + y²) = y² y = - fo Ov fi P r(2x+y) (1-²) v(22:²-²) x(1+z²)…

A:

Q: х2-х+2 7) y = *²-x+2 7) у-

A: Concept- Use the formula of d/dx (x^n)=nx^(n-1).

Q: 10. In writing a function in the denominator and its derivative is in the numerator, which of the…

A:

Q: Let = ary- + ba-y", with a and b constant. Pis a point given by (-1,-1) and it is known that (P) =…

A:

Q: use the Chain rule to find derivative: a) y = cot(412 +9) b) y = y = cos (e?) c) d) y = cos(x²) +1…

A: Solve the givens

Q: The function for a current is /(t) = 9cos 120nt where / is the current, in amperes, and t is the…

A:

Q: 1. Find each derivative. a) y = sin- X c) f(x) = ln- sin x COS X b) y = cos(x² - 2x-8)

A:

Q: 1. a) Copy and complete the table below: Original Function First derivative Second Derivative y =…

A:

Q: a) Find the derivative of the following functions: i) f(x) = x Inx ii) f(x) = iii) f(x) = 1 4* iv)…

A: Solution:-

Q: An implicit relationship between x and y is given by the equation x² + y² - 20x - 16y + 64 = 0. This…

A:

Q: Find d^2y/dx^2: y^3=6x^2

A:

Q: Find the second derivative of each item. 1. y = x° + 3x2+ 4x 1 2. y = 3. y = /(4 – x2) 4x 4. y = x +…

A: