Find dy du dy and when y and u are defined as follows. du dx dx y = 3u² + 6 and _u = x² + 2

Q: The plane x + y + 2z = 12 intersects the paraboloid z = x² + y2 in an ellipse. Find the points on…

A: Suppose the point nearest to origin with the condition that it is not the ellipse that is obtained…

Q: 1) A pump is used to fill an inflatable mattress at a constant rate of 0.25 cubic feet per second.…

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Q: six 3x sin B. Sin³ x + sinx+c Csix 3 x sinx D.six x + A B C

A: We will solve the problem

Q: Use Lagrange multipliers to find the shortest distance, d, from the point (1, 0, -2) to the plane x…

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Q: x TC Q2\ Find The Area under the curve Y= 4sine between X= and 2 X= π by the double integral method.…

A: Let's find area by using double integral method. Small mistake in given question, there should by…

Q: Find the integration by applying (by part method) f Sin-¹y dy

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Q: a. The line through the point P(3,-4,-1) parallel to the vector i+j+k. b. The line through P(1,2,-1)…

A: a) Here, the given vector is: v=i+j+k=<1,1,1> And, to find the line equation which passes…

Q: 1) In the triangle that determined by the points P.Q and R, find a unite vector perpendicular to…

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Q: MODIFIED TRUE OR FALSE. IF THE STATEMENT IS CONNECT, WRITE C. IF NOT, WRITE THE ANSWER + THE…

A: I am attaching image so that you understand each and every step.

Q: Determine the open intervals on which the graph is concave upward or concave downward. (Enter your…

A: Topic = Derivative

Q: Solve the given differential equation by separation of variables. dy xy + 5x - y - 5 dx xy - 2x + 6y…

A: We can solve the given differential equation by using the variable separable method.

Q: (x + 2) sin ydx + x cos ydy = 0

A: Solve by variable separable

Q: Q5/ Determine the total differential If Z = f(x,y) = x²y², x=2rcose, y=2rsinė

A: this is a problem of differential. Based on the general formula and concepts we will answer the…

Q: In this exercise, we estimate the rate at which the total personal income is rising in a town in…

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Q: Determine whether the differential equation (7x+8) + (7y - 7)y' = 0 is exact. If it is exact, find…

A: To determine that the differential equation is exact or not.

Q: X | J = -dx x+1 Consider the following propositions according to the integral shown: 1- When…

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Q: find a rule which describes the given numbers in the sequence 2. 1.1/8, 1/27, 1/64, 1/125..

A: Here is the solution:

Q: 3) Find equations for the lines: a 21 g. The line through (0.-7,0) perpendicular to the plane…

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…

Q: Determine if +∞o 5 dx √x-1 is convergent or divergent.

A: Solve the improper integral then using expansion at infinity solve limit

Q: Evaluate the integral dx fax √2x-x1

A: Given: I=∫dx2x-x2   As we know the common integral; ∫11-x2dx=sin-1x+C

Q: Which of the following is correct in solving 3/22 2x√2 + x dx? Trigonometric substitution can be…

A: To determine which of the following is correct in solving ∫2x2+x dx.1 Trigonometric substitution can…

Q: When does f(x) = ln(x + sin2x), 0 < x < 2π have a local minimum?

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Q: Use the law of cosines to find the angle of the triangle based off the sides listed below for…

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Q: Q3) Find the integration by using Partial fraction method Y x² + 2x + 1 (x² + 1)² dx

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Q: Evaluate the following integral. r/4 1 (s secx- cos cos sx)²dx 0 x/4 ļ (secx- cos x)²dx= 5 3 4 8 0…

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Q: Use implicit differentiation to find d²y = dx² d²y dx² if 8y+sin y = x.

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Q: Consider the function f(x) = sin(4x). a. Determine f '(x). b. Determine f"(x). c. What is the…

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Q: Y=t-2√√√x + X Find domin and ringe

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Q: The officers of a high school senior class are planning to rent buses and vans for a class trip.…

A: Solution

Q: If integration using u-substitution technique is used to solve for ∫2e2x1−e4x dx/square root of…

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Q: Consider the following statements: I. 27x+3, 27x11, and 27x + 17 are antiderivatives of 27. II. In…

A: Given : 1. 27x+3, 27x-11 and 27x+17 are antiderivatives of 272. In general, 27x+C is an…

Q: If A=(4,3,0), B=(2,3,4) and C= (5,6,2) find the dot product and find the angle between the vectors.

A: Dot product defined as  AB =|A| |B| cos x x is angle between A and B

Q: Find the extrema of the following function on the given interval, if they are any, and determine the…

A: Follow the procedure given below.

Q: b. ] ] 6x²-2x-1 3 4x -X d -dx

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Q: Name: Roll No.: Date: 1. Find the L.C.M. of x²-5x+6, x²-4x+3 and x²-3x+2 2. Find the H.C.F of:…

A: Concept: Venn diagram: A Venn diagram is a diagram that facilitates visualizing the logical…

Q: Consider the function: sit > 5 f(t) = -{² 3t si 0 ≤ t ≤ 5 To calculate £ {f(t)} using definition you…

A: We have to find laplace of given function.

Q: Using the polya's four step problem, how many square are in the figure?

A: Concept: Polya's four-step problem solving: (1). Recognize the issue.Sometimes the issue isn't so…

Q: Consider the function f(x) = (3x² − 4)(x² + 6). (a) Compute the derivative of f(x) by multiplying…

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Q: Write the relations and convert polar to Cartesian coordinates of ( 1, 45° ), then draw the point…

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Q: 7- cos y dx + (x siny-cosy)dy = 0 8- (1+ y²)dx + (2xy + y² + 1)dy=0

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Q: Find equations for the planes: d. The plane through P(2,4,5) perpendicular to the line x=5+t y=1+3t…

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Q: Certain radioactive material decays in such a way that the mass remaining after t years is given by…

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Q: Question 4 A student club is selling t-shirts for Thon every weekend. They found that when selling…

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Q: The graph of a function f is given below. JW y = f(x) X

A: from left graph of f(X) is increasing , f'(x) &gt; 0  after that slope of line is steeper ,…

Q: Q3) Find the integration by using Partial fraction method Y x² + 2x + 1 (x² + 1)² dx

A: The given integral is: I=∫x2+2x+1x2+12dx   As we know that; The Power Rule: ∫xndx=xn+1n+1+C And…

Q: Let S = { 1 − (−¹)ª | n € N}. Determine inf S and sup S. Justify. (-1)" n

A: Given : S=1--1nn|n∈N   To Find : inf S and sup S

Q: Find the plane determined L1: x=-1+t 12: x=1-4s by the intersecting lines: y=2+t y=1+2s 2=1-1-3-1-00…

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Q: Solve the triangle ABC if b = 127, c = 163, ZB = 40°. a = ZA = degrees; ZC = degrees; Assume ZA is…

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Q: Use the Laplace transform to solve the given initial-value problem. y" + 4y = sin tu(t - 2π), y(0) =…

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Q: D Question 15 Find the value of b such that the function f(x) is continuous everywhere. x² + a if x…

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