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Q: Evaluate the following iterated integral. 1 16 12y dx dy ? 0 9 Vx+y2

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Q: Find the centroid of the region cut from the first quadrant by the circle x2 + y2 = a2.

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Q: A sphere is filled with air. If the volume of the sphere is decreasing at a rate of 534 cubic cm per...

A: Given

Q: Three different parallelograms have vertices at (-1, 1), (2, 0), and (2, 3). Sketch them and find th...

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Q: Find the local extrema of the function f(x)=xlnx.

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Q: xe" – In(1+ x) is lim x2 :Select one .a 4 .b 2 .C .d 3 3 一2

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Q: Solve these

A: Part (a) Let

Q: Write an integral for the average value of f(x,y,z) = xyz over the region bounded by the paraboloid ...

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Q: 3. A rectangular bird sanctuary is being created with one side along a straight riverbank. The remai...

A: Let, two sides= x and another side= y So, 2x+y=12 y=12-2x

Q: Find the volume of the solid obtained by rotating the region under the graph of the function f(x)=2x...

A: Given:

Q: he surface of an island is defined by the following function over the region on which the function i...

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Q: (a) The curve with equation 2 y 3 + y2 - y 5 = x 4 -2x3 +x 2 has been likened to a bouncing wago...

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Q: First picture is the problem and second question is the question to the problem. Please state answer...

A: We first find the left and right hand limit

Q: Find the local extrema points of the function f(x)=(x−a)ex, where a is an arbitrary real number.

A: Consider the function

Q: (a) write formulas for ƒ . g and g . f and (b) find the domain of each

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Q: Explain why the equation cos x = x has at least one solution.

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Q: Evaluate the following integral as written. In7 7 9y dx dy X O ey

A: First, integrate with respect to x.

Q: First picture is the problem and second question is the question to the problem. Please state answer...

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Q: Find the 3rd derivative of the function y=f(x) given by the equation y2=2x.

A: Without any further delay, please proceed to differentiate and calculate the derivatives.

Q: Find the explicit solution y = y(x) for the IVPy' =2x/(y + x2*y) ; y(0) = -2

A: Given equation an be written as

Q: 44. The discriminant fufy – fw² is zero at the origin for each of the following functions, so the Se...

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and s...

Q: Need help with entirety of the question.

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Q: How is the answer -54

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Q: 6.4. 6

A: Since we are given with functions in terms of y. so we will use the first integral i.e option A. cl...

Q: The population of a city is P(t) = 2 · e0.06t (in millions), where t is measured in years. Calculate...

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Q: k 2. what is Hhe ksi 3. Sum of series and is it verdes

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Q: Sketch the region of integration and evaluate the following integral. || 12x2 dA; R is bounded by y ...

A: Clearly, Option D defines the area inside all the three curves i.e y= 0 and y= 8x + 16 and y=4x3

Q: In Exercises 27 and 28, sketch the solid whose volume is given by the specified integral. 27. (9 – x...

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Q: a) In x-3/In x +2=0 giving answer in exact form and decimal approximation to 3 decimal places

A: Given equation is Let us take, then, given equation become

Q: FIND THE FIRST DERIVATIVE

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Q: Find all derivatives of the function y=1/2x−3.

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Q: Use cylindrical shells to find the volume of the solid generated when the region enclosed by the giv...

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Q: Need help with entirety of the problem.

A:

Q: Once you know limx →a+ ƒ(x) and limx →a- ƒ(x) at an interior point of the domain of ƒ, do you then k...

A: If the left and the right-hand limits of a point are equal then the limit at the point exists. So, ...

Q: Use the Intermediate Value Theorem to prove thateach equation has a solution. Then use a graphing ca...

A: Let us consider the interval [-2,2] Let, f(x)=2x3 - 2x2 - 2x + 1 f(x) is a polynomial function, so ...

Q: Please help

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Q: Find the centroid of the boomerang-shaped region between the parabolas y2 = -4(x - 1) and y2 = -2(x ...

A: Parabolas are

Q: Let g(x) be a differentiable function such that g(−2)=0, g′(−2)=−5. Find the value of g(−1.8) using ...

A: Given g(x) be a differentiable function , g(−2)=0 g′(−2)=−5 a=-2 To find g(−1.8)

Q: use the Comparison Test to determine whether or not the integral converges.

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Q: Find the derivative dydx of the parametrically defined function x=t+2sinπt, y=3t−cosπt at t=12

A: Given X=t+ 2 sinπt and y = 3t- cosπt We have to find dy/dx at t=12 Method used Chain rule-...

Q: In Exercises 55–72, sketch the graph of the function. Indicate the tran- sition points and asymptote...

A: y=x+3 is a linear function, so it will not have any transition points or asymptotes We make a table ...