2. Evaluate J dx (cos³x sin³x)

Q: x+2, The function f(x) = 2x², Select one: Ⓒ True False x≤1 1<x<3 is continuous from the right at x =…

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Q: circle is inside a square. The radius of the circle is decreasing at a rate of 3 meters per hour…

A: Here we have to use the concept of derivatives

Q: Using Linear Approximation, estimate Af for a change in x from x = a to x = b. f(x) = ln (x), a = 1,…

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Q: If z = x - 2y, dz and x = 2t, y = 5t, then the value of at dt t = 3 is equal to -8. Select one: True…

A: To determine whether the given statement is True or False.If z=x-2y, and x=2t, y=5t, then the value…

Q: For the limit, lim (x,y)→(0,0) sin(x² - y²) x² - y² if we approach along y-axis, we will get 1.…

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Q: Find the solution of the given initial value problem. y(4) 10y""+25y" = 0; y(1) = 10 +e5, y'(1) =…

A: This is a problem related to differential equation. Please follow the procedure given below.

Q: Let 2 = (y - 2x) ³, where x = s²t and y = st². Use the Chain Rule to find when s = 2 and t = -1. Əz…

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Q: Solve the given dy=x√ e+~

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Q: 1: Evaluate the integral 3x - 1 (x + 4)(2x - 1) I -dx.

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Q: If limx-5 f(x) = 4, limx-5 g(x) = 2, and limx-5 h(x) = 18, what is the value of lim x-5 4f(x) + g(x)…

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Q: Find an equation of the plane with the given characteristics. The plane passes through (0, 0, 0),…

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Q: 32. a. b. f cos(4sinx - 1) cos(2sinx + 8) cosx dx is sin(6sinx + 7) − sin(−2sinx + 9) + C 1 1 12. 1…

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Q: Evaluate et +2e2t-et e2t +1 dt.

A: Given that a integration problem and we solve this problem by using general property of integration.…

Q: If z = √√√xy, dz and x = t², y = 1² then =? dt Select one: O √xy(21) O √xy(21²) 0 2t O None of them…

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Q: Part c: ( 1. Find the gradient of the function f(x, y, z) = ln(xy) - zx² at the point (1, 1, -1). 2.…

A: We have to find the gradient and directional derivative.

Q: x² 2 =dx 2 √4+x²

A: solution:-∫x24+x2dx=4∫x2441+x24dx=2∫x221+x22dxwe know thatcosh2t-sinh2t=1cosh2t=1+sinh2tusint…

Q: The domain of the function f(x, y) 3xy 2+√4x2+y2-16 is:

A: Given :fx,y=3xy2+4x2+y2-16

Q: 3. (y + ²+ ) dx + (x + xy²)dy = 0 3 2

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Q: A road perpendicular to a highway leads to a farmhouse located a = 1.5 km away. An automobile…

A: This question is based on application of derivative.

Q: Using the substitution u = expressed as an integral in terms of u is given by -1, the definite…

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Q: The range of the function f(x, y) [1/3, +00[ This option None of these This option ]- 00, 1/3]…

A: Here, the given function is: f(x,y)=13+x2+y2

Q: √2 2 sin-¹(x)dx

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Q: If In (x² - y) √-x+y+1 then the domain D of the function f is given by the set f(x, y) = Select one:…

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Q: 8. Find the first two non-zero terms of the Taylor expansion for function f(x)=sin x and a given…

A: Let's solve.

Q: Find sets of parametric equations and symmetric equations of the line that passes through the given…

A: To find sets of parametric equations and symmetric equation of the line that  passes through the…

Q: Let f(x) = 2x+1, if x1 O (-∞, 1) U (1,00) O (-∞0, 1] U (1, ∞0) OR O (-∞0, 1) U [1,00)

A: topic- limits and continuity

Q: f(x, y) = ln (2x) In (3y) + x - y - xy +3, then fxy(2, 2) is equal to Select one: 0 -2 None of them…

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Q: The parametric equations of the line that passes through A(-3,5,9) and B(-4,-7,2) is:

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Q: Consider the following all-integer linear program. Max 1x1 + 1x2 s.t. 5x1 + 7x2 ≤ 37 1x1 + 6x2 24…

A: As per the instruction, we will be answering the first one. Kindly post again for others. Given:

Q: 1) Evaluate the integrals: (a) f sin³ (2x) cos (2x) dx (b) sin³ (2x) cos (2x) dx

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Q: Question Select one: equals 4. None of them does not exist. equals 12. equals 0. 8x³ - y³…

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Q: If f(x, y) = 2√/16 - x² - y², then the domain of f is the set D = {(x,y)|x² + y² ≤ 16}. Select one:…

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Q: 4. fx(2x - 1)'dx

A: This is a problem related to integration. Please find the general procedure given below. As per the…

Q: Find the limit lim 3-0 Select one: 04/3 None of these Does not exist -8/6 00 8x² + 7x-9 6x²-2 if it…

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Q: Suppose that the concentration (measured in gm3) of nitrogen in the soil along a transect of land…

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Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive.…

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Q: Use left and right endpoints and the given number of rectangles to find two approximations of the…

A: Concept: Using Left Riemann Sums and Non-Uniform Partitions, a Process for Approximating Definable…

Q: If p = (7, 2), then find -2p.

A: If p=7, 2, then to find -2p.

Q: 2. Solve the following 4th order linear differential equations using undetermined coefficients: y…

A: We need to solve D.E.

Q: Bob, Trinity, and Roger are painting their living room. Trinity takes twice the number of hours that…

A: This question can be solved using the concept of time and work.

Q: A rental company charges $65 a day and 20 cents a mile for renting a truck. Michael rents a truck…

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Q: Evaluate the integral using the following values. [³x³ dx = [²x dx x³ dx = 1,020, Lºx dx = 30, [³dx…

A: use the property of definite integral.

Q: Find the coordinates of a point P on the line and a vector v parallel to the line. x − 3 _ y + 1 4 2…

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Q: Work Problem for the question. Let where x = t = -1. You must provide a clear and detailed solution…

A: Please see the below picture for detailed solution.

Q: Use partial fractions to find the indefinite integral. (Use C for the constant of integration.…

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Q: √x +3 If f(x, y) = xy + 7 the domain of f(x, y). Select one: True False then the point (1, −7) is in

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Q: Use linear approximation, i.e. the tangent line, to approximate 27.1 as follows: Let f(x)=√x. The…

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Q: (4x² - 9)72 99

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Q: swer of the following lim 2x²+6y² lim (x,y)→(0,0) x²+y²

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Q: A B - f sin(1-x) (2 cos(1-x))4 dx (2-sin(1-x)5+C 5 (2-cos(1-x)5+C 5 O A OB O O D OE None of the…

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