Use partial fractions to find the area of the given region. 12 x + 5x + 6 y -1 y 3 2 1 -1| 1 2 3 4 5 X

Q: The monthly payment is = 52 Use the monthly payment formula to answer the question. Round your…

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Q: For an object whose velocity is given by v(t) = - +4, what is its displacement on the interval t = 0…

A: Given that valocity v(t) = - t2 +4. And interval is t=0 to t=3. We find displacement on this…

Q: 10. Solve and check by integrating factor: {Integrating factor e[2(=)α = } y '+ 2 y = 4

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Q: Graph a vector, opposite to the given vector, that has an initial point at the origin. 2 8 + T…

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Q: The region R in the first quadrant is bounded by the coordinate axes, the curve y=e -5x The (exact)…

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Q: The complete graph of y = f(x) is given below. Use it to graph the following function. g(x) = f(x) +…

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Q: 1. In three-space, find the intersection point of two lines ₁ = (–1,1,3) + t(1,2, −2) and r₂ =…

A: The given two lines are: r1→=(-1, 1, 3)+t(1, 2, -2)Andr2→=(5, 3, -3)+s(-2, 1, 1) where s, t∈ℝ

Q: Consider the function: f(x,y)=3xye 8x²-8xy + y²

A: We know that, a function f(x,y) has stationary points at that points where, the partial derivatives…

Q: Evaluate sin (‡) dxdy- -π/2 cy² 1

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Q: Use a table to find the Taylor polynomial P3 (x) for f(x) = √I-T around c = 2.

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Q: fees

A: Solving the problem

Q: Find the first three terms of the Taylor series in x - a. ex. a=3

A: Given that a function f(x) = ex and a=3. We find first three terms of taylor series.

Q: 0 3 x√x² + 16 dx 2

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Q: Write the given differential equation in the form L(y) = g(x), where L is a linear differential…

A: The given differential equation is;  9y''-16y=sin(x)

Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not,…

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Q: What is the area between the curvey and the x-axis on the interval from [0, 2]? O 128T OO CAT 128 7…

A: The given curves are: y=x6   and   x-axis  on the interval  0, 2

Q: 7. A lidless large steel fuel tank is cylindrical in shape. To optimize storage in the truck, the…

A: A lidless large steel fuel tank is cylindrical. To optimize the truck, the total volume of the…

Q: 4. Determine the values of a and b such as the two vectors (2,1, a) & (b,-2,2) are a. Perpendicular…

A: We hae to find the vales of a and b for the given conditions.

Q: Solve the initial-value problem for x as a function of t. dx (t2-10t+24) dt SAN 1, (t > 6, x(9) = 0)

A: Use the separated the variable

Q: What is S₂²1² dx ? 2 1+3x² (tan¯¹ (3√√/3) — tan¯¹ (2√√/3)) ·(tan¯¹ (3) — tan−¹(2)) tan¯¹ (3√√/3) —…

A: We have to find the proper integral.

Q: 7(6x + 1)³√√x² + x (6x + 1)5 x² + x 2

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Q: Find an equation of the plane passing through the three points given P = (4, 2, 9), Q = (6, 7, 18),…

A: We have given three points as P = (4,2,9) Q = (6,7,18) R = (11,8,12)

Q: What is the approximate volume of the solid created when the region under the curve y = sint on the…

A: The solid created when the region under the curve :  y = sin(x) on the interval [0,π] is rotated…

Q: 5. f(x)=x² + 8x - 64, what's the minimum point of f(x)?

A: We have, f(x) = (x ^ 3)/3 - 9/2 * x ^ 2 + 8x - 64

Q: FIND THE INTEGRAL BY THE METHOD INDICATED: Notes: By Parts formula: 1. (BY PARTS) udv= = uv -Svdu […

A: The given integral is x(x-3)4. Integrate the integral by parts formula.

Q: Suppose f is a differentiable function of x and y, and the following applies. p(t) = f(g(t), h(t))…

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Q: 1. Solve the following DE using Variation of Parameters: (D2 + 1) y = secx tanx

A: given that (D2+1)y=secx tanx solve it by using method of variation of parameters

Q: 3. Consider the following vectors: (2,3) & (-5,1) a. Find the dot product between them b. Find the…

A: We have to find the dot product and angle between two vectors.

Q: e = exp(1) is called the exponential function. Which of the following are true?

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Q: SLO C. Use parametric equations and polar coordinates to graph, differentiate and integrate…

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Q: Find the local maximum and minimum values and saddle point(s) of the function. If you have…

A: Given that a a functio f(x, y) = x2 +xy + y2 +2y. And we find local maximum value and local minimum…

Q: Determine all values of p for which the improper integral converges. [.. 7 dx Op> 1 Op≥ 1 Op<0…

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Q: A-1²3 5. Find the determinants of A= 1 1-6 B -1 4 4 Is det|A| = -det|B|? 5 -1

A: The matrices are A = 21-1-14451-1B = 2-11-1445-11 To determine: The value of determinants of A and…

Q: find the general solution (GS) of the following initial value problem (IVP): y₁ = y₁ + 3y2 where y2…

A: The given system of differential equations: y1'=y1+3y2y2'=13y1+y2Initial conditions are:  y1(0)=12…

Q: Find the area under the curve y - area = 6xe-* for x ≥ 3.

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Q: Evaluate 8 5 3 √√3x+1 - dx

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Q: Determine the following limit: 2e 2x Him (2²-2-2) x-0

A: limx→02ex-2x-25x2

Q: Evaluate the integral. (Use C for the constant of integration.) [tan²(x) cos³(x) dx

A: let B=∫tan2xcos3xdx

Q: The following table gives the millions of metric tons of carbon dioxide emissions in a certain…

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Q: A line passes through the points A(-1, 3, 1) and B(2, 0, -1). Find a vector equation of the line. A)…

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Q: The cost function for manufacturing electric drills is estimated to be: C(x) = 3x² - 10x + 243.…

A: The cost function is, C(x)=3x2-10x+243

Q: Solve the equation by using the quadratic formula. 6y + 3 = -4y² Select one: √105 √105 Da { - 1 +…

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Q: Consider the following vector function. r(t) = (3t2, sin(t) - t cos(t), cos(t) + t sin(t)), t> 0

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Q: Lines intersect in a point in two-space but do not intersect in three-space. True False

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Q: Solve the formula for k 7k + ka a = f

A: Use multiplication rules

Q: x ¹ y ³ z ³ y ³ where r, the exponent of x, is: and s, the exponent of y, is: and finally t. the…

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Q: Find the equation of the line perpendicular to x = 3 through the point (-4, 7)

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Q: Given below are descriptions of two lines. Line 1: Goes through (−12, 50) and (−3, 14) Line 2: Goes…

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Q: Use the Chain Rule to find az/as and az/at. Z = tan(u/v), u = 8s + 2t, дz as дz 34 || || v = 2s - 8t

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Q: Making this substitution using [₁ gives us 10 sin²(x) cos³(x) dx 10 10 sin²(x) (1 - sin²(x)) cos(x)…

A: To evaluate the following integral. ∫10 sin2x cos3x dx Note: After seeing the previous solution, we…