1. Determine the area bounded by curves y = -x² + 4x + 3 and y = −x³ + 7x² − 10x + 5 over the interval 1 ≤ x ≤ 2.

Q: Given an acceleration function a(t)=, find velocity and position functions, given that v(0)= and…

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Q: Help with question 11 plz

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Q: dy dr = cos(²) +

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Q: tersection point A rectangle is to be inscribed in an isosceles right triangle in such a way that…

A: A rectangle is to be inscribed in an isosceles right triangle in such a way that  one vertex of the…

Q: 1. (3x - 2y + 1) dx + (3x - 2y + 3) dy = 0.

A: As per our guidelines we are supposed to answer only one question. Kindly repost others question as…

Q: Find the derivative of the function. <-2 g(x) = (7x² - - ² 4 4x + 7 g'(x) = 2 ((7x²-4) (28x²…

A: g(x)=7x2-44x+7-2 Chain rule: f(u(x))=f'(u(x))·u'(x)

Q: Consider the following: (5/2,1), (-9/2, 8/3) Find the distance between these points.

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Q: The answer is Blank 1. Blank 1 Add your answer Let R be the region enclosed by the curves y = x³ and…

A: The given curves are; y=x3 and y=2x2   Now find the point of intersection between the given curves.…

Q: a. Determine the Cartesian equation of the plane that has x-, y-, and z-intercepts at 2, -4, and 3…

A: Here we will find all equations,

Q: All exponential functions can be written in many forms. Write the function ƒ(t) = 9600 (2) ³ in the…

A: We have to write the function in required form.

Q: 5. 5 S x ³e x² dx

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Q: Evaluate the difference quotient f(a + h) - f(a) / h for the function f(x) = x ^ 2 + 4x - 5

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Q: Problem 2. Find an equation for the tangent line to the curve y = 2x² + x3 at x = 4. You must use…

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Q: B. Solve the following differential Equations y"" - y' = 4x³ + 6x²

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Q: 1. A parallelepiped is defined by vectors à = (2,-5, -1), b = (4, 0, 1), c = (3,-2,-2). What is the…

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Q: ? Question Classify the critical points of h(x, y) = x²y + xy² + x³y² + xy³ found in the previous…

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Q: [1 0 1. Let A = = (i) AB (ii) BA (iii)Is AB=BA? 41 2 -3 4 -5 -1 1 2 VY and B = 23 -5 0 6-2 [-1 -3]…

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Q: Find the tangent line approximation for √1 + x near x = = 5. ||

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Q: Create a table of value (use 8 values- 4 on the left and 4 on the right) and a calculator to the…

A: topic- limits

Q: Evaluate cos √6x dx using a substitution followed by integration by parts.

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Q: Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? 4 f(x) =…

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Q: 8. a. Using the vectors x = (3, 3, 1) and y = (-−1, 2, -3), verify that the following formula is…

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Q: Find the derivative of each of the following functions:- log₂ x 2. y=- X

A: The given data is: y=log2(x)x   To find the derivative.

Q: (b) n 1+ (x-1)"; r=1/e Σ(1-1) η n=1

A: Here, the given series is: ∑n=1∞1+1nn2(x-1)n Let, an=1+1nn2(x-1)n; n≥1

Q: Each side of a square is increasing at a rate of 6 cm/s. At what rate is the area of the square…

A: Each side of a square is increasing at a rate of 6 cm/s. To determine the rate at which the area of…

Q: 3. Emily is making a closed rectangular box with a square base from two different woods. The wood…

A: Use minimizing concept

Q: Ал So for sins (co COS 8 5 ¹ (1) d. dx

A: We can solve the question as below.

Q: Let R be the region enclosed by the curves y = x³ and y = 2x². The area of R using vertical element…

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Q: 2. Find the coordinates of the y-intercept of the plane (x, y, z)=(4,6,5) +s(2,3,1) + t(3,6,12)

A: To find out the coordinate of y-intercept.

Q: Use the table of integrals to evaluate the integral. (Use C for the constant of integration.)…

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Q: Evaluate the integral. (Use C for the constant of integration.) 64 + e* dx

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Q: What is the coefficient of the second term in a binomial that is raised to the sixth power?

A: Given.

Q: A population y changes at a rate modeled by the differential equation = 0.2y(1000-y), where t is dt…

A: y'=dydx=0.2y(1000-y) Solve for y in y'=0 0.2y(1000-y)=0⇒y=0, y=1000 Interval…

Q: (x² + y²) dx + (2xy + cosy) What is SN ? δη

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Q: Find the area of the shaded region. f(x) = 10x - 3x²-x³, g(x) = 0 The area is (Type an integer or a…

A: This question can be solved using the concept of  area bounded by two curves.

Q: Let R be the region enclosed by the curves y = x³ and y = 2x². The area of R using vertical element…

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Q: = 0? 5. Which of the following is a normal vector to the plane Z = a. C. n = (1,1,0) 72 = = (0,1,0)…

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Q: Applications of Differential Equations 3. A small metal bar, whose initial temperature was 20° C,…

A: Above question is solved.

Q: verity that has an inverse funci on. Then use the function and the given real number f(x) cos(6x),…

A: To find derivative of inverse function at a=1 .

Q: Q1: A. Solve the following differential equations dy 1. dx = (1 + y²) ex dx

A: You have asked multiple questions and not mentioned which question answer you need so according to…

Q: 6. Integrate the function below using Trigonometric using 6 lines only (solution + Substitution…

A: Let's solve given integral.

Q: Find a formula for the quadratic function whose graph is shown. y X 15 f(x) = -5 30 20 10 f 5 (5,2)…

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Q: The projected population of a certain ethnic group(in millions) can be approximated by p(t) =…

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Q: 2.(D5 – 2D³ – 2D² – 3D — 2) y - - = 0

A: To solve the higher order differential equation.

Q: A. [oa] a) Let A = 0 4 Find a find matrix P) diagonal matrix D so that PAP=D for some invertible…

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Q: -15 Evaluate the integral: -dz x²√²+64 (A) Which trig substitution is correct for this integral? 0x…

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Q: (2)√√2x+1 dx

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Q: A ball is thrown  vertically upward from a platform that is 60 feet high with an initial velocity of…

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Q: Solve for x accurate to three (3) decimal places ex-12=7

A: The given equation is  ex-12 = 7  Solve for x.

Q: sin X SS € y dy dx

A: To evaluate the value of given double integral.