Find the limit (if it exists). (If an answer does not exist, enter DNE.) x + y lim (x,y) → (0, 0) x² + y

Q: Evaluate the integral. Select the correct answer. 1 15 cos ²6 x - = cos 6x + C cos³6 6x- 18 O…

A: Given :∫sin36xdx

Q: Evaluate the following integral. 45 S SS²² dz dx dy -411

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Q: a T c. 10 ml Convert the following (us

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Q: 5. Which of the following represents the volume of the solid formed by revolving the region bounded…

A: Given that y=x3,y=1and x=3, about the line x=3.Using washer /disk mathodr=3-y13r=Radius of…

Q: find the limit, if it exists. If the limit does not exist, explain why. limx→2 1−|x|^2/1−x^2

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Q: Determine if the graph can represent a polynomial function. If so, assume that the end behavior and…

A: Solution

Q: Use the given acceleration function to find the velocity vector v(t), and position vector r(t). Then…

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Q: Evaluate the indefinite integral given below. Provide your answer below: f(-5x-3)³ dx = ¯ [(-5 (-5x…

A: The objective is to evaluate the integral.

Q: Given f(x) = 3x³ +22x² - Part: 0 / 2 Part 1 of 2 -21x-40, answer the following. Factor f(x), given…

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Q: A cable is to be run from a power plant on one side of a river 900 meters wide to a factory on the…

A: pythagoras theorem = H2= B2 + S2 WHERE H= HYPOTENUSE B=BASE S =SIDE

Q: Evaluate (csc 4x + cot 4x) dx 2

A: Given :∫csc4x+cot4x2dx

Q: 1. What is the slope of the line whose equation is 5x + 7y - 3 = 0.

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Q: A department of roads and highways is doing a drive, a driver's rest area on the side of a highway.…

A: Ans=200 m  For detail...go through the solution...I have done solution in detail

Q: 5. 2π π [[(sinx + cosy)dxdy πο

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Q: How much must be deposited today into the following account in order to have $65,000 in 5 years for…

A: Given :Future value =F=$65000Present value =P=?Rate = r=6%=0.06Time=t=5 years

Q: Suppose that f is integrable on [-4, 7]. If the average of f on the interval [-4, 7] is 4.25, fin 4…

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Q: lf f(x) = -[-² 0 u²-6u +5du, then what is the y-coordinate of its inflection point? Selected Answer:…

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Q: 900mL of lactated ringers is infusing at a rate of 42gtt/min.  The drop factor is 60gtt/mL.  How…

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Q: Evaluate: fx 3* dx if a is equal to the first digit and bis equal to the second digit of the sum of…

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Q: H.W: Evaluate the integral 30 J S (x²y- 0-2 1. (x²y - 2xy)dydx

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Q: Compute u v if u and v are unit vectors and the angle between them is R|4

A: we know that u.v =uvcosθfor unit vector u=v=1given θ=π4

Q: Let Vis the volume of the solid of revolution expressed by the equation V = 4n fx²e²dx. Find the…

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Q: compound proposition (PnQ)-(PUQ) is a

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Q: Find the indefinite integral. (Use c for the constant of integration.) [(4t³i (4t³i+ 14tj -7√tk) dt

A: The given integral is;  (4t3i +14tj -7(sqrt(t))k).

Q: Set up, but do not evaluate, an integral that represents the length of the parametric curve Select…

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Q: a. For the following function, find f'(a). b. Determine an equation of the line tangent to the graph…

A: To find f'(a) & equation of tangent:

Q: 10. √x(x² + 3x-8)dx A. -4 B. -404 105 D. -28 105

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Q: Solve differential equation dx -(2ln5y+x-¹) 2xy-1

A: Solution is given below:

Q: Question 1 a) Find the value(s) of y such that the vectors U₁ = and u₂ = are parallel. b) Find the…

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Q: The combined electrical resistance R of two resistors R₁ and R₂, connected in parallel, is given by…

A: To find the rate of charging.

Q: 13. 2ny(8- y³/2) dy A) 4² (14 — y³/²) + C 7 2my 7 (14-y3/2) + C C) B) T² (14+y³/2) + C 7 D) 4²…

A: 13. The given integration is: ∫2πy8-y32dy To evaluate the given integral.

Q: 2-x Evaluate: 44-3 dx A. In 4x² + 4x-31+ In 2+ 8. In 4x² + 4x-31+In+C c. In 4x² + 4x-31+In++C D. In…

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Q: Sketch the plane curve. r(t) = 3ti - tj, [0, 3] y O 2 1 -1 -2 y 3 2 - -1 -2 2 4 4 Find its length…

A: This question is related to vectors and parametric equations, we will solve it using given…

Q: 리 The amount of time in seconds, f, it takes for a bungee jumper to free fall is given by the…

A: The amount of time in seconds, t, it takes for a bungee jumper to freefall is given by the function…

Q: x+2 3.) (x²-1)(x²+1)² of factor. dx; Solve by using partial fraction. Indicate the type

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Q: The velocity function the time interval [-3,5]. article moving along a line. Find the displacement…

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Q: B)Solve the differential equation =(3+x¹)+x²e³x.

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Q: 4. What is the length of the latus rectum of the ellipse whose equation is (x-3)² + 2 = 1. 25 16

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Q: The amount of a radioactive substance, y, decays exponentially such that its half-life is 8 days. In…

A: topic- differential equations

Q: P 3. Evaluate the integral fx cos(3x²) dx as an infinite series. (You do not need to find the radius…

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Q: Use Green's Theorem to evaluate the following line integral. Assume the curve is oriented…

A: Please see the below picture for detailed solution.

Q: Find the equation of tangent line to the curve y = 2 - x 2 (7, ²/7). at the point (7, Express the…

A: The objective is to find the equation of tangent line.

Q: H.W: Evaluate the integral (x²y - 2xy) dydx 1. 30 0-2

A: As per your query the solution of the question no 1 is given in the next step.

Q: Let r(t) = (e²t, e−³,5t) Calculate the velocity vector and the acceleration vector at t = 0.

A: r(t) = ( e2t , e-3t , 5t ) given  find velocity vector and acceleration vector    velocity vector…

Q: 2. 4xx X (2-x4)6

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Q: A solid of revolution is formed by revolving about the x- axis the region bounded by the curve y √2x…

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Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by y =…

A: y = x5 y =1  find V = ?   V = π∫(f(x))2dx here we have to find limit of x  here first quadrant given…

Q: Find the lower sum for f(x) = x + 2 on the interval [0, 5] using 5 rectangles. 10 Submit your answer…

A: I appended the formula used in the solution part of the question

Q: f(t) = 4e-3t - sin 4t + cos 2t

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Q: 12. For an object whose velocity in ft/sec is given by v(t) = cos(t), what is its distance, in feet,…

A: Topic = Integration