f= 1 √√x² + y² + z² 13. Find Vf if 14. If the angle between A = xã, + â andB = V3â, +ây is 60°, find x. the vectors

Q: Calculate[ri(t) r2(t)] and [r₁(t) × r2(t)] first by differentiating dt the product directly and then…

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Q: f(x) = { 2x + 1 10 - x x < 3 x ≥ 3; a = 3:

A: Here we have to find the limit at x=3.

Q: a. Find the other functions of the triangle ABC, given that: 1. Sec A = 2 2. Cot A = 5/2

A: Solution is done in step 2

Q: f[in (w) ² ] ^ 4 3 dw

A: ∫lnω24ωdω=∫2lnω4ωdω=∫16ln4ωωdω=16∫ln4ωωdω Substitute u=lnω⇒dudω=1ω⇒dω=ωdu; 16∫ln4ωωdω=16∫u4du…

Q: Assume that x and y are differentiable functions of t. For the following, find dx/dt given that x =…

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Q: Suppose that the daily profit (in dollars) from the production and sale of x units of a product is…

A: Given that the daily profit (in dollars) from the production and sales of x units of a product is…

Q: Use the given derivative to find all critical points of f, and at each critical point determine…

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Q: Evaluate fff (3x + 2y)dV, where S is the solid bounded above by the plane z=4, below by plane z=0…

A: ∫∫∫(3x + 2y) dV=∫∫∫(3x + 2y) dxdydz = ∫z = 04∫y = -13∫x =-11(3x + 2y) dxdydz = ∫z = 04∫y = -134y…

Q: An oil slick on a lake is surrounded by a floating circular containment boom. As the boom is pulled…

A: Given: drdt= 5 m/min To find: dAdt when diameter = 140m Area of a circle with radius r is defined as…

Q: A model for the spread of a rumor is given by the equation p(t)= 1/1+ae^(-kt), where p(t) is the…

A: Given problem:- A model for the spread of a rumor is given by the equation p(t)= 1/(1+ae-kt)…

Q: 3. Find the area of the surface cut from the nose of the paraboloid x = 1-y²-z² by the yz-plane. Do…

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Q: 3 -7 [3] 7 -5 Let E= -2E= 0 Find -2E. 00 8 [000) 000 1000 [00] Undefined

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Q: Find f '(x), if f (x) = e−5x 5e O-5e^-5x 5e^-5x 5x

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Q: S dx x²-x+1 (x+1)3

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Q: Find sin 2x, cos 2x, and tan 2x if cos x = sin 2x = cos 2x = tan 2x = 0 X 3 and x terminates in…

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Q: Obtain the Lagrange interpolating polynomial for a certain function f of which we know that: f (-1)…

A: Lagrange interpolating polynomial: The Lagrange interpolating polynomial is a degree polynomial that…

Q: Use Green's Theorem to evaluate the integral. Assume that the curve C' is oriented counterclockwise.…

A: This is a problem related to vecto calculus. Based on the green's theorem we will answer the…

Q: A farmer uses x lb of fertilizer per acre at a cost of $0.20 per pound, leading to a revenue of R =…

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Q: The average cost function for the weekly manufacture of retro portable CD players is given by C(x)…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 8t, where 0 ≤ t ≤ 1. [(x + 3y²) dy

A: We can solve this as follows:

Q: 343 2 1. y = x² - 9 and y = x + 3 (Answer: 6 s. u.)

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Q: Match the vector field with its graph. F(x, y) = xi + 3yj 山供 得 三 -5+ 5 X 三 -5+ ||| 三 5 BE 州 X x

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Q: lars) from the production and sale of x units of a product is

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Q: x²+x-1 dx 5x² + x3-x

A: First we take partial fraction then solve it.

Q: Suppose that z = x²y³, where both x and y are changing with time. At a certain instant when x = 2…

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Q: Find the equation of the tangent line to the graph of f(x) = x'e- at x = 0.

A: The given function is f(x)=x9e-x at x=0.

Q: integration

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Q: Calculate the perimeter of each of the following [4] a) a parallelogram quit piece with sides 6%…

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Q: Use the given derivative to find all critical points of f, and at each critical point determine…

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Q: Find the area bounded by the given curves. y = x2 − 1 and y = 8 − 8x2        square units

A: Given :

Q: Consider the following theorem. Theorem If f is integrable on [a, b], then [ºf(x) dx = dx = lim…

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Q: dx 4 √x √x + ²+√x S

A: Here we have to solve the given integration.

Q: B с Ь

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Q: Evaluate the line integral [39a²³yzds with respect to s along the 2 curve C: x = t, y t, y = t²,₁…

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Q: 2. Determine the area of the region bounded by the curve y = x³ - x² - 2x, and a. the x-axis the…

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Q: a. b. ² (30e³P +/- ¹ dp р 4 1 2 2x4 dx

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

A: Given,             Suppose that f is integrable on -4,7. The average value of f on the interval…

Q: 1. x²y + 2xy-5y³ =0

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Q: Evaluate the integral [₁ F. dr. F(x, y) = (x² + y) i+(6x - cos y) j where Cis the boundary of the…

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Q: Find the equation of the tangent line to the graph of f(x) = x³e-* at a = 0.

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Q: Find the particular antiderivative of the following derivative that satisfies the given condition.…

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Q: 5. Consider the surface obtained by rotating the graph of f(x) = 1/2, 221, around the z-axis. This…

A: We will show this using integration ∫1∞1xdx = ln x1∞ = limx→∞ln x = ∞

Q: 4. S dx x+√2x+1

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Q: Use the method of cylindrical shells to find the volume V generated by rotating the region bounded…

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Q: Activity 3. Problem Solving. Solve the problem. Show and illustrate your solution. The ladder 7.5…

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Q: Question 20 Find the derivative of y = log₂ (x - 2)³ 1/(In2)(x-2) 3/(In2)(x-2) 2/(In3)(x-2)…

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Q: ume that x and y are differentiable functions of t. For the following, find dx/dt given that x = 8,…

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Q: Use the graph of g(t) = G'(t) below to answer the following. Make sure to show work and justify your…

A: Area above x axis is positive  are below x axis is negative ∫02 gt dt  = area from 0 to 2=16∫24 gt…

Q: As shown in the figure below, Isabel is looking at a tree that is leaning at an angle of 87° with…

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