Find the first partial derivatives of the function. || f(x, y) = gy

Q: Find the surface area of revolution about the x-axis of y = 7 sin(2x) interval 0≤x≤ ka 2 over the

A: To find the surface area of revolution about the -axis of over the interval

Q: Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = 3 sin(x) + 3 cos(x),…

A: Consider the function (a) The intervals on which the function is increasing or decreasing can be…

Q: The function f(x) = (4x + 7)e X = 3x has one critical number. Find it.

A: To find the critical number of the function .

Q: What are the projections of the point (4, -4,5) on the coordinate planes? On the xy-plane: On the…

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Q: (8) Find the value of c guaranteed by the Mean Value Theorem for f(x) = 2/²/²/1 I [3, 5]. (A) 1+ 2√2…

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: 8 Find the sum of the series Σ η = 1 20 (5η – 3)(5n + 2)

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Q: s sin x cos x dx by four methods: 64. Evaluate a. the substitution u = cos z b. the substitution…

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Q: Consider g(x) = 11 Determine the -intercept(s) of g. Report solutions in (a, g(x)) form.…

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Q: Find the Taylor polynomial of orders 0, 1, 2, and 3 generated by f at a. f(x) = sinx, a = A 4 Po(x)…

A: To find the Taylor polynomial of orders 0, 1, 2, and 3 generated by .

Q: he temperature of a person during a certain illness is given by the following equation, where is the…

A: We are asked to find extreme point of the function

Q: b. List any critical values. c. Identify intervals of increase. d. Identify intervals of decrease.

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Find two positive integers such that their sum is 28, and (a) maximize and (b) minimize the sum of…

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Q: Consider the implicit equation x²2y² = 7, where y is a function

A: x2−2y2=7ddx(x2−2y2)=ddx(7)Using the power Ruleddxxn=nxn−1

Q: Find an equation of the line tangent to the curve at the point corresponding to the given value of…

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Q: You are constructing a cardboard box from a piece of cardboard with the dimensions 2 m by 4 m. You…

A: We are given a cardboard with dimensions .

Q: A tank is full of water. Find the work W required to pump the water out of the spout. (Use 9.8 m/s2…

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Q: 3 5, x < 15. f(x) = {_x²+3, X2-1² -2x If f is the function defined above, then f'(-1) is?

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Q: Recently, a certain bank offered a 5-year CD that earns 2.34% compounded continuously. Use the given…

A: Principle amount(P) = $40,000Time of investment (t) = 5 yearsRate of Interest (r) = 2.34%

Q: Find the area of the triangle with vertices: Q(3,4,4), R(3,3,2), S(4,6,-1).

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Q: In electromagnetic theory, the magnetic potential u at a point on the axis of a circular coil is…

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Q: Complete the steps needed to find the arc length of the following function. 1 y = 2² +²e=²₁ 0≤ x ≤b…

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Q: Determine the limit of the sequence or show that the sequence diverges by using the appropriate…

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Q: Write the integral as the sum of the integral of an odd function and the integral of an even…

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Q: Glorious Gadgets is a retailer of astronomy equipment. They purchase equipment from a supplier and…

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Q: A baseball team plays in a stadium that holds 64000 spectators. With the ticket price at $8 the…

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Q: 6. Gravel is being dumped from a conveyer belt at a rate of 30 meter³/min and it forms a pile in the…

A: Diameter = height(h)radius r = h = 2rVolume of circular cone =

Q: Find equation of the tangent to the curve at the given point x=t^2-4t, y=t^2+4t+1; (0,33)

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Q: Integrate: 1 -dy 36-y y³

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Q: e. 4x + 11 +8 > 16

A: The absolute value of a number is it's distance from zero. Since distance is always positive or…

Q: Let F be the vector field F(x,y,z) = xi+yj +5ck and let S be the part of the cone z = 2 beneath the…

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Q: A clothing company determines that its marginal cost, in dollars per dress, is given by the function…

A: Given,

Q: Consider the function f(x) = 2x³ - 27x² 60x-10, -5≤x≤ 15. The absolute minimum of f(x) (on the given…

A: The given function is .The aim is to find the absolute maximum and minimum of  in the given…

Q: Improper Integrals, Infinite Limits of Integration: Integrals may have infinite limits of…

A: The given integral converges.

Q: If ƒ(x) = 3x² – 3eª, find:

A: f(x)=3x2−3ex

Q: Find the absolute maximum and minimum values of the function over the indicated interval, and…

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Q: on Find the absolute max and min values. given interval, the of fixel if any, and state where those…

A: Given,

Q: You are constructing an open top box for your cat to sleep in. The plush material for the square…

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Q: Find r'(t), r"(t), r'(t)r"(t), and r'(t) x r"(t). r(t) = 2t²1 – 3tj+t³k (a) r'(t) (b) r"(t) (c)…

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Q: Practice 1: f(x)=√x X+1 fferentiate and simplify your answer:

A: The given function is

Q: First make a substitution and then use integration by parts to evaluate the integral. √r π/2 0³ cos…

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Q: The altitude of a triangle is increasing at a rate of 1 centimeters/minute while the area of the…

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Q: 00 Consider the series Σ (19x)" n=0 (a) Find the series' radius and interval of convergence. (b) For…

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Q: Use any method to find the relative extrema of the function f(x) = 20x + 7x7. If there is no…

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Q: Select the integral that gives the area bounded by f(x) = sin (2x) and g(x) = cos(x) over the…

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Q: Find sin theta and cos theta, if tan theta = -3 and theta terminates in Q3.

A: Note:-Since you asked multiple questions, according to our policy we can answer only first question…

Q: Given the equation below, find dy dx -33x³ +855y + y³ y = = dy dx - 24 Now, find the equation of the…

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Q: If cos x = 4/5, csc x < 0, then sin 2x cos2x = tan 2x

A: Cosx=4/5 ,cscx&lt;0

Q: The function P(x) = -2.5x² + 775x - 9500 gives the profit when x units of a certain product are…

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Q: Let f(x) = x³ + 6x² + 1. Calculate the derivative f'(x) = 3x² + 12x Calculate the second derivative…

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Q: Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x4 50x² + 3 (a) Find…

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