Find a polynomial equation that passes through the points (1,3), (0,1), (1,3)

Q: y^2dx + (x^2 + 3xy + 4y^2)dy = 0; when x = 2 , y = 1

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Q: Find the point of inflection of the graph of the function. (If an answer does not exist, enter DNE.)...

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Q: Evaluate the following using trigonometric substitution: Vx2 - 4 dx

A: Find your answer below 

Q: A 500 gallon tank initially contains 50 gallons of brine solution in which 28 pounds of salt have be...

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Q: Evaluate the given integral by changing to polar coordinates: Sl. x²y dA, where D is the top half of...

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Q: 15.

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Q: A chemical substance has a decay rate of 9.5% per day. The rate of change of an amount N of the chem...

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Q: Question 6 Find all the second order partial derivatives of the given function. f(x, y) = x y 2 + y ...

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Q: (x²-ax +4" dx

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Q: Differentiate each function with respect to x. 2. y = (-3x5+ 1)3 3. y = (-5x3 – 3)3 4. y = (3x3 + 1)...

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Q: Write the first three terms of the sequence. 3n - 2 n2 +2 The first three terms are a1 ,a2 = and a3 ...

A: Given ,an=3n-2n2+2Put n=1a1=3(1)-2(1)2+2a1=3-21+2a1=13,Put n=2,a2=3(2)-2(2)2+2a2=6-24+2a2=46,a2=23,a...

Q: Compute for the dot product between the following pairs of vectors. Also, using the dot product alon...

A: We can find the dot product and other required answers as below.

Q: Question 12 Provide an appropriate answer. Find when r = 4 and s = 3 if w(x, y, z) = xz + y, x = 5 r...

A: We will put the values of x,y and z in w(x,y,z) to convert w in the terms of r .

Q: 4. (2y cos x + sintx) dx sinx dy 5. y' = 1 + 3ytanx %3D

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Q: The region bounded by the curve x=y?, the y-axis, and the line y=2 is revolved about the x-axis. Fin...

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Q: Find two vectors in opposite directions that are orthogonal to the vector u. (The answers are not un...

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Q: 6.1 f*, V16 – x² dx 4

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Q: Find the derivative of the function at Po in the direction of u. f(x, y, z) = In(x 2 + 3y 2 + 9z 2),...

A: Since you have posted multiple questions i can do first question as per our company guidelines pleas...

Q: 1. y (x3 +3)5

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Q: 3. Consider the series n (2л — 1)8п. - п4 + 1 n=1 Use the previous item to find its interval of conv...

A: Solution is given below:

Q: If y = csc² x+ 2 , then ſ y dx = cot x + 2x + c True O False

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Q: Consider the pair of savings plans below. Compare the balances in each plan after 13 years. Which pe...

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Q: Voter Registration The amount of voters in a city's district should grow at the rate of 1500 / (8 ...

A: at present it is = 25000 after 2.5 year so t =2.5 growth = 1500/(8 + (2.5)2 )0.5  growth = 1500/(8+6...

Q: fV5+ 4x – x² dx

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Q: The sales, S. of a product have declined in recent years. There were 204 million sold in 1984 and 1....

A: The sales, S, of a product have declined in recent years. There were 204 million sold in 1984 and 1....

Q: Given the curve y = x² – 2 and line x = y. 1. Compute the area bounded.  a. 3.2 sq. units b. 2.6 sq....

A: Since you have asked multiple question, we will solve the first question for you as per our guide li...

Q: Consider the given function and the given interval. f(x) = 5/x, [0, 4] (a) Find the average value fa...

A: The objective is to solve the above question.

Q: The functionf is a continuous function with the following characteristics: f(x) <0 on the interval -...

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Q: Every year, Danielle Santos sells 29,880 cases of her Delicious Cookie Mix. It costs her $1 per year...

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Q: The table gives values of a continuous function. Use the Midpoint Rule with three subintervals to es...

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Q: (b) Oppositely directed to 6i – 4j + 2k. 6 i v = V56 2 k + V56 V56 (c) Same direction as the vector ...

A: Given problem:- Find unit vectors that satisfy the stated conditions. (b) Oppositely directed to 6i-...

Q: 5. Use the comparison test to determine if each integral converges or diverges b) 2 2/3-4 a) e-x² dx

A: Solution: 5.a ∫1∞e-x2dx

Q: 2n +1 Σ n n tan-1 n n=1

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Q: An object is released from rest, at a height of 1250 feet above the ground. The height of the object...

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. ...

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Q: Question 1 A puck of soap makes a perfect cylinder It is submerged in water and begins to dissolve, ...

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Q: Sketch the region enclosed by the given curves. y = x* - 15x?, y = x? 20 4 40 -6 -2 6 2 -20 20 -6 -4...

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Q: dy + xdx + 2ydx = 0

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Q: Evaluate the integral. dx J x4+7 Inx) A In 14+7 In x| +C B In 14+7 In x| +C © O In +C |7+4 In x| D I...

A: On solving this we will get:- option (D) is correct

Q: MY NOTES Find the volume V of the solid obtained by rotating the region bounded by the given curves ...

A: Topic = Volume

Q: Find the area of the region between the curves

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Q: (За — 1)" 5n Vn + 1 n=1

A: Given problem:-

Q: f(x) = 6x/(1 + x²)², [0, 2] %3D (a) Find the average value fave of f on the given interval. fave = (...

A: Question- f(x) = 6x/(1+x²)², [0, 2]   (a) Find the average value (fave ) of f on the given interval....

Q: f(x, y) = x2 + Sxy + y2 O f(8,0) = 64, local minimum; f(0, 8) = 64, local minimum f(0,0) = 0, saddle...

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Q: . In (3xy) %3D х+ x5

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Q: dx

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Q: 2. Show that the equation 2x + cosx 0 has exactly one real root.

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Q: Solve the derivative: sinx – 1 F(x) = COSX Answer: sec(x)tan(x)(sin(x) – 1) -

A: We will find the derivative. 

Q: 21. |'t cosh t dt Jo

A: Note:- These are multiple question and according to our company guideline we can do maximum one ques...

Q: Recycling Programs The commissioner of a particular city's recycling program assesses that the amoun...

A: for 2008 here t = 8 so put t = 8 in equation N(t) = (200,000)/(2.5 + 3e-0.5t) N(8) = (200,000)/(2.5 ...