4 P = 80x-2x²-xy-3y² +100y + X(12-X-Y) FinD Px, Pxx, Py, Pyy, Pxy = Pyx, fino x And y Fine Fine P

Q: ∫cos(7t) dt Evaluate indefinite anti-differentiation

A: LetI=∫cos7tdtPut 7t=uDifferentiate on both side7dt=dudt=du7ThereforeI=∫cosu17duTake the constant…

Q: Two years ago, $5, 000.00 was placed into an investment in which the amount of money present, P,…

A: To find the amount of investment after 15 years from now.

Q: (8x4 − 5x2 + 2)dx evaluate indefinite anti-differentiation

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Q: Find the area of the shaded region. = √cos 20 9 cos X r

A: Area = integration of 1/2 (r2^2 - r1^2) d(theta)

Q: sin $3xcos 3x dx

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Q: Find the average value ha of the function h on the given interval. ave h(u) = (14 - 13u)-¹, [−1, 1]…

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Q: f sin √x dx

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Q: Verity Green's Theorem by evaluating both integrals ƏN [x² dx + x² αy = [] (2 - 0) A √y² dy dA ax ду…

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Q: ∫ sinx √cosx dx

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Q: d³y d²y dy+y=0 dx3 dx² dx

A: d3ydx3-d2ydx2-dydx+y=0                (1)LetD=ddxTherefore   equation (1)…

Q: A plane flying horizontally at an altitude of 3.4 miles and at a speed of 790 mi/hr passes directly…

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Q: = fx x²zdx- dx − yx² dy + 3 dz along the curve C shown in the figure. - Z 2 2 [x²zdx - yx² dy + 3 dz…

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Q: 6.S dx √1+√√x

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Q: 1 x² + 8x + 5 x3 + 12x2 + 15x + 6 dx

A: Solution of given question is written in below steps.

Q: State the coordinates of the intercepts, stationary points, and the inflection point of p(x) = 2x³ -…

A: Here we have to use the concept of derivatives

Q: Let f(x) = 3x5 - 5x³.

A: The given function,   f(x)=3x5-5x3

Q: 3. The Bernoulli's form of the differential equation x³ydx+(3x¹-y³dy=0 is

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Q: A farmer uses x lb of fertilizer per acre at a cost of $0.20 per pound, leading to a revenue of R =…

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Q: Use the given derivative to find all critical points off, and at each critical point determine…

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Q: 10 F [TOF If f(x) dx = 16 and 5 Isro f(x) dx 10 f(x) dx = 5, find the following. S

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Q: Consider the following. y 4 y=x³ - 2x -2 y = 2x (a) Find the points of intersection of the curves.…

A: This question is based on definite integral.

Q: Identify and sketch the graph of the equation in R³. x = 1 − log₂ y

A: This is a problem related to graphing the function. Based on the general formula and concept we will…

Q: Plot the curve c(t)=(2t−1,²+3). Then find the length of the curve for 1<t≤2 to two decimal places.

A: Curve is ploted and length of curve is obtained.

Q: Find the equation for the tangent and normal lines for f(x) at the specified points. Show your…

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Q: 2.S x² -4 X -dx

A: Note: Asper company guidelines, we are supposed to answer the first question only. Kindly ask the…

Q: Find the total mass of the wire with density p whose shape is modeled by r. r(t) = t²i + 2tj + tk,…

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Q: Verify Green's Theorem by evaluating both integrals for the given path. [x² αx + x² or = // (+1) ++)…

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Q: Find dy dx 1. y = (3-2x)³ (x² − 2)

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Q: Solve the differential equation y' = 6x³y² subject to the condition that y = .1 when x = 1. y(x) = =…

A: We have to find the solution

Q: A county's statistics indicate that the number of white-collar crimes is growing according to the…

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Q: * (2 √x (2+x) dx

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Q: 6. Use Green's Theorem to find the counterclockwise circulation and the outward flux for the field F…

A: This is a problem related to vector calculus. based on the general formula of green's theorem we…

Q: (3x+4)2dx Evaluate indefinite anti-differentiation

A: The given integral is (3x+4)2.

Q: The finate finear pattern 20;17;14...-103.Calculate number of terms in the sequence ?

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Q: xy + 1 lim (x, y)→(1, −1) x² − y²

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Q: Find the indefinite integral. (Use C for the constant of integration.) I Sil sin 20 de

A: 2θ=tdθ=dt2I=12∫ sin4t  dtI=12 ∫ sin t sin3t dt =12∫ 3sint -sin3t4sint dx=38∫ sin2t dt-18∫sin3t sint…

Q: Find the indefinite integral and check the result by differentiation. (Use C for the constant of…

A: Here we have to find the indefinite integral.

Q: Use the given derivative to find all critical points of f, and at each critical point determine…

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Q: Find the differential dy: y = In (sec² (3ª²–2x+5)).

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Q: Evaluate Ic (2x - y) dx + (x + 3y) dy. C: arc on y = x5/2 from (0, 0) to (4, 32) X

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Q: Itiple 1. Which of the following is the maximum value of the function f(x)=2 sin.xcos.x? a. 2 c. √3…

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Q: 8) A rectangle has a perimeter of 8 inches. What should be the dimensions so that its area is a…

A: Given query is to find the dimensions for maximum area.

Q: [ sin³(2x) dx

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Q: 4. S dx x+√2x+1

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Q: Determine the general equation of this differential equation. xy³ dx + e*dy = 0

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Q: For a non-negative function f(x), an approximating formula for the area under curve using a uniform…

A: The area approximation formula is Area≈∑fci∆xi=1n. Where fci=Height of the ith rectangle   ci…

Q: 1. The minimum possible perimeter for a rectangle with an area of 529 m² is

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Calculate[ri(t) r2(t)] and [r₁(t) × r2(t)] first by differentiating dt the product directly and then…

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Q: ∫12v (7+6v2)9 dv Evaluate the following integral using substitution rule or integration by…

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Q: (b) 3, 1, 1 1 1 3'9' 27

A: