Use Green's Theorem to evaluate the line integral. S y² dx + xy dy C: boundary of the region lying between the graphs of y = 0, y = √x, and x = 25

Q: Find the exact length. T=0², 0≤0 ≤ 2π ° 4[G²+1²] ²3 [(x² + 1)² - 1] [(²+1)-1] ° 4[68² +1²]

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Q: Find the two x-intercepts of the function f and show that f'(x) = 0 at some point between the two…

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Q: V. Given: -2, if x ≤2 f(x)-[2x-5]. if 2 3 1. Determine if f is continuous or discontinuous at z=2…

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Q: Find the derivative of the function. f(t) = (9t+ 9)2/3 f"(t): =

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Q: Below is the graph of altitude A(t) for a balloon that is rising and falling. 15,000 A(t) 10,000…

A: In the given graph we have to determine tmin and tmax

Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. 2. lim (√x²-x-√x² + x)

A: Please see the answer below.

Q: Ex. (8) Sol Solve [D²-6D+9] y = 54x+18

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Q: Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of…

A: As per Bartley guidelines we are supposed to answer only three subparts of one question per post.…

Q: If f f(x) dx = 12, then ff(4x) dx is equal to If f f(x) dx = 12, then fx f(x²) dx is equal to

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Q: Integrating Factor by Inspection: 7. xdx + ydd = (x² + y²)dx

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Q: Give the properties for the equation x 2 +y 2 + 4x + 6y - 12 = 0 Domain -3 ≤ x ≤ 8 -5 ≤ x ≤ 5 -7 ≤…

A: We can find the domain of the equation as below.

Q: 1. F = cos y i+ xyj + yk, A B C D E F О н A. i+j+(y-siny)k B. i+ (siny - y)k C. j (2y-siny)k D. 3i -…

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Q: Find an equation for the parabola that has its vertex at the origin and satisfies the given…

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Q: 7 What is the probability of getting two heads and one tail when a coin is flipped three times?…

A: solving

Q: A continuous F(x1= 글X K value V-V- 15 X x has CDF 16 X Co OBX C1 15X k of 17 18 19 20 21 An

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Q: 6. Use Green's Theorem to find the counterclockwise circulation and the outward flux for the field F…

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Q: 8 sin 8. Then sketch the curve.

A: The correct curve of r = 8 -8sin(θ) is  Option (C)

Q: Find the value of d²y/dx² at the point defined by the given value of t. x = sint, y = 7 sint,t=4 14…

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Q: A new fish species is introduced into a lake. Assuming that the population of fish quadruples in the…

A: Solved below

Q: Suppose f is continuous everywhere, f’ is differentiable everywhere except at x = -1, and the graph…

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Q: Solve the given initial value problem. O x¹y² - xy³ = = 84 x³y² - y² = 26 x¹y² + xy³ = 78 x³y² + xy³…

A: Let's find.

Q: 4 Identify the center of the conic section whose equation is x 2 +y 2 + 6x - 4y - 12 = 0. (-6, 4)…

A: The given equation is; x2+y2+6x-4y-12=0   As we know that; The general form of equation of the…

Q: Find the length of the curve. (Hint: u-s

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Q: Replace the polar equation with an equivalent Cartesian equation. r² = 44r cos 0 (x-22)² + y²-0…

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Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

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Q: Give the properties for the equation 3y 2 - 2y + x + 1 = 0. Latus Rectum

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Q: Find the derivative of the function. h(t) = - (²²) ² h'(t) =

A: We have to find derivative

Q: SKETCHPAD Write the formula to represent the nth term of the following sequence. 6, 17, 34, 57, 86,…

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Q: Find the limit. lim → 2 (1 i=4j+ 1² k) i. lim 1-2(ti-4 j+¹² k) = + j+ k

A: evaluate the limit component wise

Q: Find the fourier transform of x*arctan(x) x*tan^-1(x)

A: Solution of the problem as follows

Q: a = a What is the 150th term of a A 151 B 152 с 309 D 311 n-1 +2 if a₁ = 11₂

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Q: Write TRUE if the statement is correct, otherwise write FALSE. y y = h'(x) (-3,0) (3,0) x (0, -1)…

A: To write TRUE if the statement is correct, otherwise to write FALSE. Suppose that hx is continuous…

Q: d'y dx² d²y + dy dx X=

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Q: f(x,y) = 3x-2y. R÷ the circle x² + y² = 1

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Q: 3. lim x 3 (x-3) tan(9-x²) sin (2x-6)

A: Explanation of the answer is as follows

Q: Find the volume of the th

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Q: 7T 2 Find 35 cos(7x) dx 5π 2 7T 2 35 35 cos(7x) dx = -5π လ

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Q: Consider the function y=x³ - 9x + 4. a. Sketch the graph of y= x³ – 9x + 4. b. Find and describe the…

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Q: Sketch a right triangle corresponding to the trigonometric function of the acute angle 8. sin(8) - 1…

A: Using the properties of trigonometric functions we find the given values

Q: Using production function Y = K1/2 1/2 and using the information below: Relative to US column 4…

A: Solution of the problem as follows

Q: Find u v, uu, |v||2, (u v)v, and u. (3v). . u = 8i + j - 3k, v = i - 4j + 3k (a) u. V (b) u. U (c)…

A: This question is related to vectors, we will solve it using given information.

Q: 2 Find the center of the following equation.      x 2 +y 2 + 8x - 6y - 15 = 0 (4, 3) (8, -6) (-4,…

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Q: . Evaluate the following limits. Using L'Hôpital's Rule is not allowed. 4 4. lim loga (x+3)…

A: limx→1-log12(x+3)1-cosh(cos-1x)=limx→1- log2-1(x+3)1-cosh(cos-1x)since, limx→af(x). g(x)=limx→a f(x)…

Q: 1 of x only, then = 0 (x) dx ne given equatio 2 21

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Q: area enclosed by enclosed by the Curve Find the X = 2y² and x = 8

A: This question is based on application of integration.

Q: 1) fx-²dx 2) sin(n)dx

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Q: Find T(t) and N(t) at the given point. π r(t) = 4 cos(t)i + 4 sin(t)j + tk; t = 2 4 1 T(+7) = -√17 Т…

A: given  as you have already found Tangent vector

Q: Find an equation of the plane with the given characteristics. The plane passes through the point (1,…

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Q: NE- My Ne If = Q, where is a function of y only, then the differential M equation M + Ny = 0 has an…

A: ydx+3xy-e-3ydy=0

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

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