75 Compute the definite integral cos³ (2x) sin² (2x)dx . 4 30 2 15 1 15 6 775 10

Q: π Compute the definite integral cos³ (2x) sin² (2x) dx .

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Q: 3. Determine an equation in symmetric form of a line parallel to *³ = = = 2+2 and z+7 3 -4 passing…

A: We have, given line equation: (x - 3)/3 = (y - 5)/-4 = (z + 7)/4

Q: Find the indefinite integral. Hint: u = x - 1 implies x = u +1. x(x-1)dx

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Q: 5. Consider the following function: f(x)= e* (3x³) a. Determine the critical points of such function…

A: For a function f( x ) , we can find  critical points by f'( x ) = 0  Inflection points by f''( x ) =…

Q: 9. The region R enclosed by the curves y = √√x and y = x² is rotated about the x-axis. Find the…

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Q: 13. For f(x) = -x³ + 3x² + 9x, find the followings. a) Find f'(x) and the critical points. b)…

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Q: A separable differential equation is a first-order differential equation that can be algebraically…

A: Separable differential equation = ?

Q: 3. Use the Fundamental Theorem of Calculus Part I to determine the derivatives of the following: (i)…

A: We need to solve Integral problem.

Q: Calculate the integral approximations Tê and M₁ for ſå xª dx. Your answers must be accurate to 8…

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Q: Consider a right triangle with a side of length opposite angle A, a side of length y opposite angle…

A: Given: Consider a right triangle with a side of length x opposite angle A, a sideof length y…

Q: (b) J₁ In x x3 dx

A: To determine whether the following integral is convergent  or divergent.  ∫1∞lnxx3 dx Note: Since,…

Q: forin the egral. ayus 4. Perform the line integral for 0 ≤ t ≤ 1. where the cur is the straight me…

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Q: Evaluate the given definite integral. 6 x√x-6 dx

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Q: e(4²)* + e* (4²*) (4)* + 4° dx

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

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Q: Solve the following differential equations dy dr² dy -9x+24y=0, y(1)= 1,y(1) = 0 dx

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Q: x7-9

A: We know that the integral of x^n dx= x^(n+1)/(n+1)

Q: Use the graph of F to find the given limit. When necessary, state that the limit does not exist. lim…

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Q: 4. Evaluate √xe-²x² d

A: ∫xe-2x2dx

Q: (a) Find the intervals of increase or decrease. (b) Find the local maximum and minimum values. (c)…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 15. a) Find the limit. x²-9 lim x--3x²+2x-3 b)lim √25+h-5 h

A: (a) let H=limx→-3x2-9x2+2x-3

Q: f f(0) = - = sin(1-0) Sketch the graph of f(0) = -

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Q: Use the graph and the function to find the following. a) Find lim k(x). x--1 b) Find k(-1). c) Is k…

A: limit existance conditionif LHS limit = RHS limit continuity existance conditionif LHS limit = RHS…

Q: The marginal profit is given by MP= P'x = x(90x+2x^2). Find the total profit function.

A: To find the total profit function, we need to integrate the marginal profit function with respect to…

Q: Solve for the unknown quantities, if possible, in Exer- cises 5-16. 5. (1, 2) + (0, y) = (1, 3)

A: Note:- Since you asked multiple questions, according to our policy we can solve only first question…

Q: 33 ow your work and explain, in your own words, how you ar relevant explanations may receive reduced…

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Q: Integral is convergent or divergent. Evaluate those (c) (d) S 2² 9+x6 dx

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Q: -10 x f(x) 10 10 Use interval notation to determine where f(x) ≤ 0. (0,1) 10 Use interval notation…

A: A graph is given and we need to find out the intervals.

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: If you want to earn 15% annual simple interest on an investment, how much should you pay for a note…

A: Simple interest Formula is given as  SI = P×R×t100 Where P is the principal amount  R is the rate of…

Q: ∞0 (x+1)" n=1 Vn4n

A: Use the Ratio test

Q: 3. A parallelogram is formed by the vectors OA = (6, 3) and OB (-1, 1). Determine the acute angle…

A: A parallelogram is formed by the vectors OA→=6, 3 and OB→=-1, 1.   To determine the acute angle…

Q: Let f(x) = 2x³ - 3x² - 72x+1. a. Find all points on the graph of f(x) at which the tangent line is…

A: Let fx=2x3-3x2-72x+1 (a) To find all the points on the graph of fx at which the tangent  lines are…

Q: Use implicit differentiation to find дz дх дz ду || || 9yz + x In(y) = 22 z2 X дz дх and дz ду

A: By using the implicit differentiation to find ∂z∂x and ∂z∂y. 9yz+x lny=z2

Q: 7. Sketch the region enclosed by the given curves and find its area. y = sin x, y = cos x, x = 0,…

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Q: etermine the moment of force F about point A. = 260 N swer: M₁ = (i 0.55 m 0.50 m i+i j+ i k) N-m

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Q: -5 y 30 20 10 f 5 (5,2) 10 15 20 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 = (5,3,…

A: The point of intersection of two lines is a common point on both lines, it has same x,y and z…

Q: pls solve within the time given. and make sure it is 100% correct thanks, Determine the concavity…

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Q: Find f(x) by solving the initial value problem. 5 f'(x) = 1 +e²+ = f(1) = 7+e f'(x)=1+e*+

A: Given: f'(x)=1+ex+5xf(1)=7+e We are required to find: f(x)

Q: Find the indicated partial derivative. V = In(r4 + s5 + tº); Ꭷ3v ərəsət Ꭷ3v ərasət

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Q: Find the exact solution for e2-2e-35=0. 2x If there is no solution, enter NA. Enclose arguments of…

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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: Self-Assessment 8) Suppose you measure the length of a house to be 60.50 ft. How many yards is that?…

A: according to bartleby guide line we do only first part of multiple questions  given length=60.50 ft…

Q: What is the product of 5 and 1.0\sqrt(72) in simplest radical form? Please explain, correct answer…

A: 172 = 136*2           = 1(36)*2          =  162 now we rationalize it         = 162* 22         =…

Q: Find two unit vectors that make an angle of 60° with  v = 3i + 4j.

A: We are required to find: Two unit vectors that make an angle of 60° with  v = 3i + 4j.

Q: Perform the indicated integration using RATIONALIZING SUBSTITUTION 3 dy 4 + ³√y+1 1.f.

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: f(x) = 5 + 54x − 2x³, [0,4]

A: According to question,Given Function,fx = 5+54x-2x3,In interval 0, 4

Q: Find the area of the shaded region. NO y=0 2 2 y = x^3 - 4x^2 6 8 HH 10

A: The equation of the curve is y=x3-4x2 and y=0

Q: Calculate the integral approximations To and Me for (Inx)-¹dx. Your answers must be accurate to 8…

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