Q2: Solve the following integrals: (1) 7x²+14x+15 (x²+3)(x+7) dx ; (2) sin6 x+cos6 x sin ³ x cos³ x dx (3) √√√dx 4-x² ; (3) 7 dx (4) fxe¯* dx

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) xy - 25 lim (x, y) → (5, 5)…

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Q: Given F(x) below, find F'(x). Provide your answer below: F(x) = I 4 (414 + sin* (t)) dt

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Q: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

A: The given set,     S=1,2,3,4, 1,0,1,2,3,8,11,14

Q: (B): If A = 2i +3j - 4k; B = 3i - 4j+5k and C = i + j-k, find: (iv) (3A + 4B).C (i)A.B (ii) B.C…

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Q: Sketch the function. v(x) = 0.2(x-3)²(x+2)³ Part 1 of 4

A: In this question, we will plot atleast six points to sketch the given function.

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: k [[ x=0&y=0 x cos(xy) dydx =

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Q: 2 The function f(x) ==, x0, is one-to-one. X Find an equation for f(x), the inverse function. ...…

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Q: cos¹3 xdx 2. Dễ sin12xcos®xdx 1.

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Q: Given the equation 5 sin 6xy = 3, evaluate dy Assume that the equation implicitly defines y as a…

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Q: (B): Find the unit vector perpendicular to the vectors: 3i - 4j+5k 4i + 5j-6k ;

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Q: 3. The marginal revenue function has x measured in years and MR(x) in hundreds of dollars per year.…

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Q: cise (a) e volume of the solid formed by revolving the region about the x-axis 01 he region is…

A: To find the volume of solid revolving around x axis using disk method

Q: 2. 01 S -1-1 (x+y+1)dxdy

A: The Solution is given below

Q: Question: 9 a)Use the second derivative test to determine whether the function has a local maximum…

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Q: (B): Find the tangent equation to the curve y = sin² x at point x =

A: I have stated the used formulas in the solution.

Q: Describe the level curves of the function. z=x+y, c= -2, 0, 2, 3 O The level curves are parabolas.…

A: We need to choose correct option.

Q: B)Evaluate the integrals: i) √1-x2-x²-y² ii) -² ²-²-² dz dy dx. xe dy dx.

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Q: 4. 4 1 [x²ydxdy 20

A: I have stated the used formula in the solution

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: A box with a square lid uses a material for the lid and bottom that costs $ 4.00 per square meter,…

A: We can solve the given problem by using the second derivative test.

Q: Find the limit. lim (x,y) → (5, 1) ety Discuss the continuity of the function. O continuous…

A: See this solution in below

Q: Given the space curve r(t) = (2 cos 2t, 2 sin 21, 31), find the unit vectors, 4 B

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Q: Exercises L- If H B =). 33" 3 14. BB+A-SI-D E A-

A: The answer is given below:

Q: QUESTION 1 Let I = fxe³x. To solve I, we need to apply O Integration by substitution O Integration…

A: The answer is given below.

Q: Given: f(x) = 0.2 + 25x-200x^2 +675 x^3-900 x^4 + 400 x^5 from a = 0 to b = 0.8 and segment equal to…

A: Given that      f(x) = 0.2+25x-200x2+675x3-900x4+400x5   from a=0 to b=0.8 and segment equal to 8.…

Q: Find the mass and the center of mass of the lamina with density 8(x, y) = √y x² +1 the rectangular…

A: We have the following formulas(i)  Mass of a region m=∬δ(x,y)dA, where δ(x,y) is the density and dA…

Q: Find both first partial derivatives. z=(4 xy)/(x^2+y^2) fx(x,y)= fy(x,y)=

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

A: Here we will find the slope of given line,

Q: Consider the points A=(1,2,3), B=(-2,1,0), and C=(0,3,1). Adding the vectors, find 2AB+3AC.

A: To find 2AB +3 AC

Q: (A): If A = 4 2 -2 Find AB and AC. 2 1 -1 2 3 11 0; B= 2 -2 -2 and 1 l-1 2 1. 3 1-31 C=02 6 l-1 2 1

A: A=420210-2-11B=2312-2-2-121C=31-3026-121

Q: fe e sin xdx

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Q: 1. Solve the following a) 430.00(1+0.05) b) 1.2:4.2:60= 5 45 4 64 c) y: 9 8 (1+0.05)³3 -1 0.05

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Q: eliminate the arbitraty constats of the differential equation y = C1e^2x + C2xe^2x a. y” + 2y’ + y =…

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Q: (B): Find the tangent equation to the curve y = sin² x at point x =

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Q: The following table shows the daily receipts in millions of dollars of the movie "Avatar" for…

A: Consider the points 19,0.633,21,0.335,23,0.12,25,0.064 and 27,0.044. Find the Average rate of change…

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

A: Topic = Volume

Q: s 32x² (x-15) (x+5)² dx I

A: Integral

Q: 1) Consider the DE: xy' +(5x-1)y = 0. A) Determine whether the DE is linear or nonlinear and find…

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

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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: We have to find out equation of tangent

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: 7√2 2 0 x² 49-x² dxl

A: The given integral,        ∫0722x249-x2dx

Q: (B): If A = 2i +3j - 4k; B = 3i-4j+5k and C=i+j-k, find: (ii) B.C (iii)A. (B+C)and (A + B).C (iv)…

A: Given: A→=2i+3j−4k;B→=3i−4j+5k and C→=i+j−k We know that x1i +y1j+z1k·x2i +y2j+z2k = x1x2+y1y2+z1z2

Q: Find the limit. lim (x, y) (1, 56) √x + y √x + y Discuss the continuity of the function. O…

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Q: A rectangular box with an open top has a length of x feet, a width of y feet, and a height of z…

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Q: Find the antiderivativef e* sinxdx A.je*(sinx – cosx) + c C. e*(sinx — cosx) + c Find the…

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Q: A submarine begins to descend at 9 meters per minute. It begins 15 feet underwater. A. Write a…

A: 1 metre= 3.281feet

Q: What is the distance between two points (3,-1) and (-2,-5). 3

A: Given that the two points (3,-1) and (-2,-5)  To find the distance between the two points.

Q: J 4 sin xecos* d.c

A: