Exercises 1. Integrate each of the following functions with respect to r: (a) rº, (b) r'/2, (c) r3, (d) 1/x*, (e) 4, (f) VI, (g) etz

Q: /v – 2ve" - 29. f(v)

A: Differentiation

Q: the temperature (in F) at point (x,y)(measured in miles) is given by  T(x,y)=80-x4 +2x2 y-y2 How…

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Q: If z = x + jy, then O Check whether the function f(z) : 1 is an entire function. State the reasons.…

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Q: Consider the function f(x, y, z) = xy+yz² + xz*. Find the gradient of f: • x+z? 2yz +3z²x Find the…

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Q: Find f'(2), where f(t) f'(2) = = u(t) · v(t), u(2) = (1, 2, -1), u'(2) = (9, 1, 6), and v(t) = (t,…

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Q: 1. At the point (1, -1), the function (z,y) has a derivative of b in the direction toward (3, 1) and…

A: Given  that at the point (1,−1), the function f(x,y) has a derivative of 5 in the direction toward…

Q: Write f(z) in the form f(z) = u(x, y) + iv(x, y). a) f (z) = z^3 b) f (z) = 1/z^2

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Q: Determine the two-variable function F(x, y) if Fy (x, y) = y sin(xy) + x given that x-² F(x₁ - ²) =…

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Q: Your used Chevy’s gas mileage (in miles per gallon) is given as a function M(s) of speed s in miles…

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Q: Use implicit differentiation to help you find the value of the gradient for the equation x² – ev =…

A: given equation x2-ey=yx-2+8 claim- use implicit differentiation to help you find the value of the…

Q: * 31² +t+4 dt t' +t

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Q: Differentiate Find y' Show all work

A: y=3xlog3x

Q: - Find and sketch the domain of the functions: √x+y+1 x-1 b) f(x, y) = x ln(y² - x) c) f(x, y) =…

A: The given functions, a) fx,y=x+y+1x-1b) fx,y=xlny2-xc) fx,y=6-3x-2y We have to find the domain of…

Q: Find f'(3), where f(t) = u(t) · v(t), u(3) = (1, 2, −1), u'(3) = (8, 1, 6), and v(t) = (t, t², t³).…

A: The given functions and function values are .The aim is to find the function value .

Q: f(x,y) af ?x af ду = af ду X 2x² + 8y² f(x, y) = tan af ?x (5)

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Q: If f(x) f'(x) = = x2 - 3 - t² dt then

A: ∫xndx=xn+1n+1+cdxndx=nxn-1dconstantdx=0

Q: Check the following functions if Piz) exist not and find f'(z) if exist: ,or D fcz) = 1Zit %3D

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

Q: Determine if f(x, y) = xe*-y + 100y is increasing or decreasing at (-2,1) if a) we allow x to vary…

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Q: The temperature on a cubic box [0, 4] × [0, 4] × [0, 4] (measured in meters) can be described by the…

A: Function, Tx, y, z=x2y+y2z

Q: For the functions below, what is the direction of fastest increase at  (1, 1, 1)? (a) f(x,y,z) =…

A: The direction of fastest increase for a function at a point is the direction of the gradient of that…

Q: Let r(x) = f(g(x)) and s(x) = g(f(x)), where f and g are shown in the figure. Find r'(1) and s'(4).…

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Q: f(z)=ze^tz/z^2+1 for this function find the Rez(f(z),i) and Rez(f(z),-i) .

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Q: We learn how to derive the MRS from a utility function, U(x, y), using total differentiation. Write…

A: An utility function is given by, Ux, y. The objective is to derive an equation for MRS by…

Q: If y=x^(2)+81, find the relationship between (dy)/(dt) and (dx)/(dt) Where x,y depend upon t.

A: We have to find the relationship between  and where  and  depend upon .We use Chain Rule to answer…

Q: Let f(x)=(x+4)^3. What are the gradient and equation of the chord/secant between (2,f(2)) and…

A: Given function fx=x+43 The formula for finding the gradient of the chord that passes through 2…

Q: Integrate by change of variable, ∫∫R(x + y)e((x^2)-(y^2))dA, where R is the rectangle enclosed by…

A: We need to evaluate integral.