Assignment: Consider the region bounde by the parabolas: 2 2 y = x + 4x + 3 and y = x + 2x + 3. A. Find the area of the region.

Q: If a company's marginal revenue function is MR(x) = xe-x/2, find the revenue function. [Hint:…

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Q: Find an explicit solution of the given initial-value problem. dy_y2. = y(7) = 7 y = dx حمد

A: Given: dydx=y2-1x2-1,y(7)=7 We are required to find: The value of y.

Q: Find all the first and second order partial derivatives of f(x, y) = 6 sin(2x + y) — 2 cos(x − y).…

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Q: Use the graph of the function f shown to the right to find f(-4), f(-3), and f(-2). f(-4)= f(-3) =…

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Q: Let F(x, y, z) = (P(x, y, z), Q(x, y, z), R(x, y, z)) = (y cos(x) — y, sin x +2yz − x, y² + 1) be a…

A: To show that the vector field F = (P, Q, R) is conservative, we need to demonstrate that its curl is…

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Q: 1 The equation of the line that goes through the point (7, 9) and has slope can be written in the…

A: The equation of a straight line passing through the point x1,y1 and having slope m is given by…

Q: Use the limit comparison test to determine whether an = n=12 an lim = lim n→∞ bn n-x n=12 (a) Choose…

A: We have to to Check the convergence of given series.

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A: Given :- At $420, A manufacturer sold number of televisions are 1150. And at $21 rebate offered to a…

Q: Consider the following. dz Find by using the chain rule. (Enter your answer in terms of t.) dt dz dt…

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Q: Evaluate the double integral changing to polar coordinates. ¹/1₁ (² (2x - y) dA, where R is the…

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Q: What is the largest number that uses each of the seven Roman numerals exactly once?

A: To find the largest number that uses each of the seven Roman numerals exactly once.

Q: An aircraft (at Z) is spotted by two observers (at X and Y) who are L = 1200 feet apart. As the…

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Q: The series Σ n=1 convergent. (-1) " n 0.9 Select one: O True O False Give your reasons is absolutely

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Q: Find the arc length of y = (*2²)* + over [1,4]. 2(x+2)² (Use symbolic notation and fractions where…

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Q: Given the set of parametric equations of a curve C defined by [0,5). x = ln(cost), y = sint, te 1.…

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Q: Use the chain rule to find əz Əs z = (x - y)², x = s²t, y = st² дz at = and az z =…

A: ∂z∂s = ∂z∂x×∂x∂s using chain rulewhere∂z∂x is partial differentiation of z with respect to x keeping…

Q: Evaluate the following integral S 4x cos (5x) dx=

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Q: If the velocity of a moving object is t 2 1² v (t) = 20 2 in meters per second, then what is its…

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Q: a) lim (-2x¹) = 8118 ) lim (-2x¹) = xx ) lim -√x = 118

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Q: Simplify the following numbers and write them in standard form: a. (4√-16+2 (150) -2(-4+3 (205)

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Use the chain rule to find the indicated partial derivatives. x4. x² + x²y₁ x = s + 2t - u, y = stu…

A: To find partial derivatives of z w.r.t. s,t,u   Given z=x4+x2yx=s+2t-u and y=stu2

Q: if √x ≤ f(x) ≤ 4₁ x + 1 for all the positive x-values, then what is lim P(X) ?

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Q: Solve the given differential equation by separation of variables. (ex + 1)²e-y dx + (ex + 1)4e¯x dy…

A: ey+12e-y dx + ex+14e-x dy = 0

Q: Calculate the linear combination. (Give an exact answer.) X = y = 6(4j+2k) - 4(2i + 7k) = (x, y, z)…

A: The vector is given by 64j+2k-42i+7k = x, y, z To determine: The values of x, y, and z.

Q: A cylinder shaped can needs to be constructed to hold 600 cubic centimeters of soup. The material…

A: A cylinder shaped can needs to be constructed to hold 600 cubic centimeters of soup. The material…

Q: Q1: Solve the following equations system, using Gauss elimination method 4y1 + 2y2 +3y3-5 =6 3y₁ +…

A: We need to solve the given system of equations using the gauss elemination method which uses the row…

Q: Q4/ For the following three matrices : k 4 k A= 0.5 2k 0.5 2 8 2k 1 3 B=m 2 1 m a- Find value of (k)…

A: Given: A=k4k0.52k0.5282k,B=13m21m,C=22161184432 We are required to: a. Find the value of k if A is a…

Q: Set up an integral representing the area A of the region enclosed by the given curves. y = 5x, y =…

A: The area between the curves y=f(x) and y=g(x) from x=a to x=b is given by the integral…

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Q: Complete the table. f(x) = X f(x) ( - 11/1 x + 0 -3 -1 0 1 3

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Q: Solve the given equation 3e*+2 = 75

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Q: 5. Use the Limits at Infinity Theorem and limit laws to evaluate lim f(z) where 818 16-² f(x)=…

A: fx=16-x26x2-5x+4

Q: d. f(x)= sinsin (2x) coscos (x)

A: To differentiate the following function. fx=sinsin2xcoscosx

Q: Find all the second partial derivatives. f(x, y) = xy - 4x5y² fxx(x, y) = fxy(x, y) fyx(x, y) = =…

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Q: Find the cosine of the angle between the vectors (1, 1, 1) and (8, -7, 12). (Use symbolic notation…

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Q: Rpup (hur +81 0=1²² x=h₁ б E I =

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Q: ƒ(x) = x + 1 X

A: fx=x+1x

Q: Each of the following problems addresses a course SLO for Math 21. Each individual student completes…

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Q: I have a few questions: How did you get from (sin2(x)+sin(x)+5sin(x)+5)/(sin2(x)-12) to…

A: Given:f(x)g(x)=sin2x + 6sinx + 5sin2x - 12   Basic information: 1. x2 + a+bx +ab =x+ax+b2.…

Q: Write the following expression as a single definite integral of the form f(x) dx. [²_1(x) dx + [³1x)…

A: Given expression is ∫-22fxdx+∫25fxdx-∫-2-1fxdx

Q: ) Based on your experience in parts (a) and (b), conjecture an antiderivative for each of the…

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Q: Evaluate the definite integral. 1 e² + 8 o e² + 8z dz

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Q: The demand function for device model PWX641 is given by p(z) = 510-0.792², where p is the unit price…

A: Given demand function  p( x ) = 510 - 0.79x2 Given data  dpdt = 6 dollarweekp = $194

Q: Find the area of the Polar Region located in the interior of the graph of r = 8 - sint A = 2√²/²2…

A: The polar equation r=8-sint Graph

Q: Find an explicit solution of the given initial-value problem. x2dy dx =y-xy, y(-1) = -4 y =

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Q: L (4 + √36-x²) dx

A: Evaluate the definite integral  We know that the formula int_a^b f(x) dx=int_b^a f(x) dx

Q: How do I use the chain rule to find the derivative of (y=(cosx+2sinx)8)? I know (cosx=1) and…

A: Chain Rule of differentiation: If y= f(u) and u=g(x) , then y=f(g(x)) , so then                 dydx…

Q: Given the function f(x) = −2x³ +96x +1, determine the intervals where the function is increasing and…

A: f(x)= -2x3+96x+1 We have to find interval of increasing or decreasing of function and also interval…

Q: consider the region bounded by the parabolas: y=x² + 4x + 3 and Find y = - x² + 2x + 3 the area of…

A: The region bounded by the parabolasy=x2+4x+3 and y=-x2+2x+3