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Q: Find the volume of a solid obtained by rotating the region under the graph of the function x = √y…

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Q: Evaluate d2y/dx2 at the point (0, -9). x = t3 - 3t y = 3t2 - 9

A: Given: x = t3 - 3t y = 3t2 - 9

Q: 2. Use Green's theorem to evaluate fe e-x³ dx + (5x + sin(y²)) dy, where C is the circle x² + y² = 4…

A: Please see the below picture for detailed solution.

Q: How do you know when the system of equations is solved? None of the answers are correct When one…

A: The objective of the question is choose the correct option.

Q: find are length x=2t² y = 3t²,0 ²t ²√58 [0,√8]

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Q: Jacob's father is planning to open a savings account to pay for Jacob's college education. He has…

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Q: OS ng n Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of…

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Q: Evaluate the definite integral 8 2x² + 7 √x -dx

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Q: ·bounded by x² + 2y = 4 and and determine: - Sketch the area x+y+2=0

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Q: Find the volume of the solid obtained by rotating the region enclosed by the curves y = and y = (Use…

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Q: r³+3x+1 8) (x+1)²(x-2)²

A: The objective of the question is determine the partial fraction decomposition. Note -  As per our…

Q: 3. Find the domain of f(x) = = 1 - 1- x X

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Q: a. b. C. d. G++++ 3 +++++:+). 3

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Q: When a consumer has quantities, ₁ and ₂, of apples and oranges respectively, his utility is given by…

A: Concept: Lagrangian function : The initial problem is reformulated as a result of the link between…

Q: For the following exercises, consider a pizzeria that sell pizzas for a revenue of R(x) = ax and…

A: Given,           Rx=7x and Cx=160-2x+x2To find : How many pizzas sold maximizes the profit.

Q: e Find the volume generated by revolving the area enclosed by the loop of the curve y² = x (x-3)²…

A: Solution is given below:

Q: 10. Find function that satisfies the given conditions: f"(x)=6x³-3x+4, f'(1)=-3, f(1) = -6

A: The function satisfies the condition f''x=6x3-3x+4, f'(1)=-3, f(1)=-6 use the integration formulas,…

Q: ● ftans (x) sec (x) dx M

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Find the exact average value fave of f(x) = √25 - x² between 0 and 5, then find an exact number c in…

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Q: Which of the following is the standard form of a circle?

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Q: The equation for the conic section with focus (x, y) = (c, 0), direc ricity e 1, by choosing c =…

A: Topic:- geometry

Q: Consider the region bounded by x=4-1², the y-axis and the x-axis. N 1 1 2 3 4 The volume of the…

A: Given problem:-

Q: Factor x^2 + 10x + 12. (x + 5) (x + 7) (x + 10) (x - 12) None of the answers are correct; this…

A: Given: Factor x2+10x+12

Q: Find the absolute maximum and the absolute minimum for the function f(x)=e−x−e−5x,…

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Q: Use the Ratio Test to determine whether the series is convergent or divergent. 00 Σ n = 1 Identify…

A: To use the ratio test so that we can determine the convergent and divergent of the given series.

Q: -3x²+tan(3x-5) Explain the steps you would take to find the derivative of f(x) = (e

A: Our Aim is to find the derivative of f(x)=12e-3x2+tan3x-5 -(i)

Q: 5. Use the divergence theorem to evaluate the surface integral ff, F. ds, where S is the sphere x² +…

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Q: Find the area of the region bounded by the graphs of f(x)=x^3-x^2+10x and g(x)=-x^2+26x

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Q: 4. Evaluate the line integral f x siny dx + y dy, where C is the arc of r(t) = ti + t²j from point…

A: Line integral

Q: What is the slope of the tangent line to the curve y=−2x^2+8x+2 at the point where x=5?

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Q: Prove that lim 12 √16x +9y¹2 2 6 4x² +3y does not exist by showing that the limits along different…

A: We have to prove that  limx, y→0, 0 16x4+9y124x2+3y6 does not exist.

Q: the area of the ellipse 9x^2 + 8y^2 = 72 answer: 26.7

A: To Find: Area of the ellipse  9x2+8y2=72

Q: A tank contains 70 kg of salt and 2000 L of water. A solution of a concentration 0.0175 kg of salt…

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Q: Given that the graph of f(x) passes through the point (8, 4) and that the slope of its tangent line…

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Q: Use the rules for sums of powers of integers to compute the sum. 24 4.² k=8

A: Recall: sum of squares of n integer                    ∑i=1ni2=n(n+1)(2n+1)6

Q: (a) Find a unit vector u from the point P = point Q (17, 34). = NOTE: Enter your answer in the form…

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Q: The base of a solid is the region in the xy-plane between the the lines y = x, y = 4x, x = 1 and x =…

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Q: A writer wrote 850 words on the first day, 730 words on the second day and 610 words on the third…

A: Given: A writer wrote 850 words on first day, i.e. d1=850 Similarly for second and third day…

Q: 2 Transformations of Exponential Functions transformations of f(x) = ab*h+k compared to f(x) = b*.…

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Q: CALCULATE THE AREA BETWEEN THE GIVEN FUNCTIONS. DEVELOP THE PROBLEM WITH ALL STEP EXPLAINED AND…

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Q: An inverted pyramid is being filled with water at a constant rate of 50 cubic centimeters per…

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Q: 3. Give an example of a situation in which composite differentiation might be used. Give examples of…

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Q: [2 2x log 2x dx

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Q: On Integration of Rational Fractions. Distinct linear factors Repeated linear factors

A: Given So we do partial fraction to get Distinct linear factor and Repeated liner factor

Q: Find the inverse of f(x) = = 1 7x-3 at x = 1. Simplify your answer.

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Q: 7. For the following system of equations, find the values of x, y, and z using the matrix inversion…

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Q: . For each positive integer n, define an = n² sin +∞ 1. Determine if the sequence {an} converges or…

A: The solution is given below

Q: Graph the equations and shade the area of the region between the curves. Determine its area by…

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Q: Typically, an inequality can have how many solutions? Multiple solutions One only solution…

A: An inequality is defined on a particular region.

Q: Find the derivative of the given function. COS ³ (1) g(x) = 2 cos3 O a) g'(x) = -3 cos² (sin() Ob)…

A: Given, g(x)=2 cos3x2