5. 3√√xdx 6. S dx dx 7. S- X 8. f s 2dx 3 2x -10

Q: Q4A) Find area bounded by y = 0, y = √x - x² using double integration.

A: Solution given below

Q: Q2A)Matrix 4 = [],find Eigen values of 4². A

A: The given matrix is  A= 1342. We have to find eigenvalues of A2. Eigenvalues are the roots of the…

Q: Find all the second partial derivatives. V = e4xey Vxx = V xy v Vyx Vyy = = ||

A:

Q: ■ Show that the area of the triangle whose vertices are the [X1 У1 points (x₁, y₁), (X2, Y2) &(X3,…

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Q: B. Given that f(x) = {(-2,1), (1,4), (2,5), (3,6)} g(x) = 6 + 4x h(x) = -x² + 2 find

A: given

Q: Q4A) Find area bounded by y = 0, y = √x - x² using double integration.

A:

Q: 4 Find the coefficient of the given term when the expression is expanded by the binomial theorem…

A: Find the coefficient of x2y7 in (2x+3y)9 using binomial expression.

Q: Find y': y=V5+2 — 2 O y = 7-2x 2√5+2x-x² Oy = √2-2x 1 Oy = 2√5+2x-x² 1-x O y = √5+2x-x2

A: We have to find derivative of given function.

Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of…

A:

Q: y = 7 cos(x), y = 7 - 7 cos(x), 0 ≤ x ≤ π

A:

Q: 16. Using the Quotient tanx= sinx/cosx to prove d/dx tanx=sec2x

A: Quotient rule of differentiation

Q: Suppose that the total profit function for a company is given by P(x) = 4x³ - 210x² + 3600x - 200,…

A: We have to choose correct option for given questions.

Q: At point (1,-1,2). 4

A:

Q: Use implicit differentiation to find y' and then evaluate y' at (-1,1). 3 x Iny+4y= 2x³ y'l(-1,1)=…

A: We have given  xlny+4y=2x3  Find y' and y' at (-1,1)

Q: Find , given y = 5² 6n² a dy dx

A: ddx(5x6ln2(x))We know that…

Q: If g(x, y) = x² + y² 6x, find the gradient vector Vg(1, 6). Vg(1, 6) = -4,12 Use the gradient vector…

A: Given that , gx,y=x2+y2-6x find the gradient vector ∇g1,6 and tangent line to the level curve…

Q: Given f(x) = 3-5x³, use a table to estimate the slope of the tangent line to f at the point P(0, 3).…

A: According to question,Given Function,fx = 3-5x3P0, 3Qx, fx

Q: 2 2(x + 1).In(x ² + 2x + 3) x²+2x+3 $² A) In(x²+2x+3) + c dx = ? B) In²(x²+2x+3) 2 +C

A: According to question,Given Integral,Let I =∫2x+1 lnx2 + 2x + 3x2 + 2x + 3 dx

Q: -)Find volume of body from above Z=√√4x² - y² and below Z Triple integration. 1 using

A:

Q: 5 Find the coefficient of the given term when the expression is expanded by the binomial theorem. x6…

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Q: coplanar.

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Q: Determine whether there is a relative maximum, a relative minimum, a saddle point, or insufficient…

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Q: Consider a beam of length L with a fulcrum x feet from one end (see figure). There are objects with…

A: Consider a beam of length L with a fulcrum x feet from one end see figure. There are objects with…

Q: Find y': O 2(x + 1)(x + 2) ○ (x + 2) (3x + 4) O (x + 2) (3x + 2) (3x + 4)(x + 1) y = (x + 1)(x + 2)²

A:

Q: Consider the following equations. 3 y = 9- -1/2x², y = X₁ x = -2, x = 2 Sketch the region bounded by…

A: Here we have to find the area and the graph of the functions.

Q: The graph of the function 86 f(x) can be obtained from the graph of y = f(x) by one of the following…

A: Solved below.

Q: Q1A)The vectors A = 3i+j+ 4k, B = 2i-3j-k, find vector normal to A and In plane of A and, B.

A: See the details solution in below

Q: Which of the following is a solution of the given initial-value problem? y' + (tan(x))y = 5 cos²(x);…

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Q: Əw 1. If w=x" f() show that x ax +y Əw ду = nw where n = integer.

A:

Q: Find the domain of the following function. 1 f(x) = 2 25-x

A: Given function f(x)=125-x2we know that fraction abis defined when b≠0the function is not defined…

Q: Find the area of the shaded region. y y=8x-r 15 (6, 12) 10 A y=2x 2 4 6 Step 1 To find the area…

A:

Q: A ship leaves its port and sails on a bearing of N35°30'E, at speed 24.8 mph. Another ship leaves…

A: This question is related to cosine formula of traingle , we will solve it using given information

Q: 3. Derivative of g(x) = 2x + xª − 7x² +3 b) 12x³+4x³ - 14x +3 c) 12x6 +4x² - 14x²_____d) 12x³+4x³ -…

A:

Q: Find an equation of the tangent line to the graph of y = x³ - 3x - 1 at the point (2, 1).

A:

Q: The marketing research department of a computer company used a large city to test market the firm's…

A: This question can be solved using the concept of maxima and minima.

Q: You are driving a car away from home. Your velocity (miles per hour) t hours after noon is given by…

A: you are driving a car away from home.your velocity t hours after noon is given by,…

Q: Evaluate: S (5 — 2 sec 0 tan 0) de - O 0.79 0.68 O 0.95 0.84

A: ∫π6π4(5-2secθtanθ)dθ

Q: A graph consisting only of a vertex is a complete graph. True False

A: Recall:  The complete graph on zero/one nodes is a trivial graph also known as the null…

Q: A kite is 30 ft. high and is moving horizontally at a rate of 10 ft./min. At what rate is the string…

A: Calculate the rate in the following way:-

Q: Bonus ( Show that given R: x € [0,1] Ay € [0,2] [[3x²yexydy dx = 6

A: See this solution in below

Q: In a Northwest Washington County, the speeding fines are determined by the formula: F(s) = 14(s -…

A:

Q: B)ls w = Ze² analytical function or not?

A:

Q: B)Is w = Zez analytical function or not?

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Q: Evaluate the integral. 1 -3 6²3 16 + r² dr

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Q: )

A:

Q: Question 10 Given z = (e-22) (sin y), find 92 O-2e-2 O-2 e 2 (sin y) + e-2 (cos y) O-2e-2 (sin y) -2…

A: We have to find derivative of given term.

Q: Cos de 1-Sin e

A: To evaluate: I=∫cos3θ1-sin θdθ=∫cos2θ×cos θ1-sin θdθ=∫(1-sin2θ)cos θ1-sin θdθ=∫(1-sin θ)(1+sin θ)cos…

Q: Find the producers' surplus at a price level of p = $61 for the price-supply equation below. p=…

A:

Q: 1 Find equation of plane which is containing Points A(2,1,1) and B(7,5,2) and normal to 2 x - 3y -…

A: We have to find the required plane

Q: 2. Which of the following sets of ordered pairs could be part of a linear function? F II (0, 1), (3,…

A: