(2a+1)(x–2) lim x00 (3x-1)(x+2

Q: dy (х — 1) — у + 2(х — 1)3 dx

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Q: Verify Green's Theorem by evaluating both integrals an_ am | v² dx + x² dy = dA ây for the given…

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Q: Find the area bounded by the indicated curves. y = 3x + 3, y = x2 + 3 Optional For visualization,…

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Q: V a(x) = e(x-5) - b(x) = -(x – 8.38)² + V c(x) = 1

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Q: Which integral corresponds to the volume of the solid generated by revolving the region enclosed by…

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Q: Take

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Q: y" + 2y' + 5y = 4e¬t cos 2t, y(0) = 1, y'(0) = 0

A: Given:       y''+2· y'+5· y=4 e-t cos2t      y0 =1   ,    y'0=0

Q: Determine the exact area between the x-axis and the curve defined parametrically by ¤(t) = ;t2 1…

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Q: Find curl (2z i + 3x j + 5y k). url(2z i + 3x j + 5y k) = ( i )i + ( )j + ( 3 )k

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Q: O f(-1) = 3, lim f(x) = 3, lim f(x) = +∞ O f(-1) = 3, lim f(x) = -o∞, lim f(x) = +o0 O f(-1) = 1,…

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Q: Express the derivative in "subscript" notation. NOTE: Your answer should take the form fo. dy dx?

A: Consider  ∂3y∂y∂x2=

Q: Find the value of n in the following definite integral. " 4x° dæ = 1 Answer: 1

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

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Q: Find V × (V × F) if F(x, y, z) = 9xyj+10xyz k. V x (V × F) =|

A: We have to find given expression.

Q: Let 7 (t) = Find 7'(t) F'(t) -

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Q: Complete the squares and locate all absolute maxima and minima, if any, by inspection. Then check…

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Q: Find r'(t), r"(t), r'(t) - r"(t), and r'(t) x r"(t). r(t) = 2t2i – 3tj + t3k (a) r'(t) (b) r"(t) (c)…

A: To find r'(t), r"(t), r'(t).r"(t), r'(t)×r"(t).

Q: given poim arctan(2) f(x, y) = arctan (4, -4) f(X, y) = x, ) = (4, -4) = (4,-4) =

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Q: [y sxy dy is equal to -y cony - J cony A (B у сoly - coty dy Scory dy C у coly + -y coty + J coty D…

A: Solution is given below..

Q: Find the volume of the solid generated by revolving the region about the given line. The region in…

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Q: 3. Find the values of x of the curve y = 3x where y' = y" 15

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Q: Describe the graph of the equation. r = 15 sin 18t i + 15 cos 18t j O It is an ellipse in the…

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Q: Find the absolute maximum and minimum values of f(x, y) = (x^2)y of the set D = {(x, y): x ≥ 0, y ≥…

A: To find the maxima and minima first diffrenciate and then equate it to zero.

Q: Let F(t) = < 5t + 5, t - 2t, 2 In < 5t' + 5,f – t, a. Determine the coordinates of the point on the…

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Q: e?y - dy (ve)" – 1

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Q: Find the general solution of the following: 1. (4D2 – 4D + 1)y = 0 %3|

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Q: L 3a da = 65 Select one: O True O False 2Vada = 104/3 %3D Select one: O True O False L(z +4)(z +3)dz…

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Q: Describe the graph of the equation. r = (7 – 21) i+ 101j O Itis a line in 2-space through the point…

A: Equation

Q: A stone is thrown vertically upward from the ground with an initial velocity of 128 ft/sec. How long…

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Q: Solve the given differential equation by separation of variables. csc(y) dx + sec2(x) dy = 0

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

Q: The integral tan x sec?x dx is an improper integral of type I that diverges none of them is an…

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Q: Find a set of parametric equations for the tangent line to the graph at t = to. (Enter your answers…

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Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 10 –…

A: Because the parabola is symmetric to the y-axis, the rectangle must also be symmetric to the…

Q: Find three positive numbers whose sum is 48 and such that their product is as large as possible.…

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

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Q: 5) Find the linear approximation to estimate V7.429. Compare this to the true value and determine if…

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Q: A local pond can only hold up to 51 geese. Seven geese are introduced into the pond. Assume that the…

A: This is a problem related to differential equation and exponential function. Based on the general…

Q: Find the indefinite integral. (Use c for the constant of integration.) (4t³i + 12tj – 8Vik) dt Need…

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Q: nd and of the following equation then simplify whenever possible. dx dx2 x = 3em y = 2mem

A: Given query is to find derivative of the expression.

Q: pe of a trail at a distance of x miles from efinite integral of f(x) from x=3 to x=5

A: answer is in next step

Q: Find the magnitude and direction angle of the given vector. 5. u = (-10, 24) 6. u = (-5, -12) %3D n…

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Q: Total cost from marginal cost. Shelly's Roadside Fruit has found that the marginal cost of producing…

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Q: Using appropriate substitution | sec*x dx is equal to In|secx + tan x| -1 + C 2cos?x + sec x tan x +…

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Q: Find the curvature and the radius of curvature at the point t = 0. x = e' cos(t), y = e' sin(t), z =…

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Q: Find an equation of the largest sphere contained in the cube determined by the planes a 1, a = 7, y…

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Q: The temperature T in a metal ball is inversely proportional to the distance from the center of the…

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Q: ||r'(t) × r"(t)|| Use the formula k(t) to find k(t). ||r(t)||* 3 r(t) = e*i+e*j K(t)

A: First diffrenciate. And then put all the values in formula.

Q: Using Long (Euclidean) division then decomposition into partial fractions x4 – 4x2 – x – 3 | dx х2 —…

A: We have to find value of given indefinite Integration.

Q: Find the partial derivative. revIlzy

A: We can find the partial derivative as below.

Q: Find the standard equation of the sphere with the given characteristics. Center: (-1, -9, 6) Radius:…

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