45. S sin x sin 2x dx

Q: 15. S sin²a da

A: The given integration is: ∫0∞sin2α dα  To evaluate the integration.

Q: Find a parametric representation for the surface. The part of the cylinder y² + z² = 9 that lies…

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Q: y = 5x² y = 0 x = 2 (a) the y-axis (b) the x-axis

A: Given  a.  about y axis

Q: 5 for 5: Calculus AB Day 4 3 1 12 -1 0 -1 jf'(x) -2 33 1 AB2: Let g(x) = f(x)f'(x). Find g'(4). AB3:…

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Q: 17. S₁- 1 x² + x dx

A: To find integral.

Q: Suppose f(x) = 7x²+5x. Find: ƒ'(1) =

A: Given: f(x) = 7x2+5x

Q: Mark each statement as true or false. a.) If a function is differentiable at x=3, it must be…

A: Topic = Application of Derivative

Q: Find the maximum rate of change of the function f(x, y) = = 4y+ X at the point (3,5)

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Q: Given the function f(x) = 2x² − 3x + 1. f(x+h)-f(x) Find the difference quotient, h a) Find f'(x) by…

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Q: Find the x-value at which f is discontinuous and determine whether f is continuous from the right,…

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Q: 2. Find an equation of the tangent line to the curve at the given point. = cosx — sinx, (T, -1) y

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Q: Which of the following have the same meaning as "the derivative of fat x=5"? ƒ(5) - f(x) 5-x lim 0-x…

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Q: The total cost (in hundreds of dollars) to produce x units of a product is 2x - 1 5x+8 C(x) = Find…

A: The total cost (in hundreds of dollars) to produce x units of a product is Cx=2x-15x+8. To find the…

Q: The sum of the arithmetic series: t2 = 8, t5 = 9.5 and n = 12 is equal to

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Q: Given: z = x² + xy¹, x = uv² +w², y=u+vew дz δω Find when u = — −3, v = −2, w=0

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Q: Solve the given differential equation by separation of variables. dy 2y = - (²x + 2)² 8x dx

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Q: Calculate the indicated limit. If the limit does not exist for any reason type DNE. sin(6x) lim x->0…

A: limx→0sin(6x)x2+3x

Q: π Find the absolute maximum and minimum of the function f(x,y) = (16x - 4x²) cos y on the…

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Q: Find the absolute maxima and minima of the function on the given domain. 13) f(x, y) = x2 - 2x - 2y2…

A: Given function is  f(x,y)=x2-2x-2y2+2y And closed triangular region is bounded by the lines x=0,y=3…

Q: The owner of a video store has determined that the cost C, in dollars, of operating the store is…

A: The cost function give in the question is C(x)=2x2-26x+620

Q: 6. Find the magnitude of the resultant of two vectors and v. given -2. -7 and the angle between the…

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Q: sequence of 10 letters from 10 A 10 8 10 C A code a) How many? (b) Even number of A and odd number…

A: Since you have posted a question with multiple sub-parts, we will provide the solution only to the…

Q: 1 □ 10. If log; (x) = 17, what is the value of log₁/3(x)? 0 1 17 317 0-17 O 10¹7

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Q: Evaluate the integral. J." 5 sin²(t) cos^(t) dt

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Q: let f(x) = 4x-2, and g(x)= 5x² - 3 find f(g(x)) = ? 20x²-2 © 4(5x2-3)-2 O 5(4x²-3)-2 O none of these…

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Q: 10. g(x)= x² +5, 10, 1+x³, x 2; x = 2.

A:

Q: Find the general solution of the given differential equation. y' = 4y + x² + 9 y(x) Give the largest…

A: Given

Q: If f(x,y)=8x2-3xy4+y4/2y fy(x,y)=

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Q: 8. Water runs into a conical tank at a rate of 8ë ft³/min. The tank stands point down and has a…

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Q: Solve the given differential equation by using an appropriate substitution. The DE is homogeneous.…

A: See the details solution in below

Q: Solve the given initial-value problem. The DE is a Bernoulli equation. x2 dy dx - 2xy = 6yª, y(1) =…

A: Use substitution  z = 1/y3  Then it is converted into exact differetial  equation.

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) xy - 4 lim (x, y) (4, 1) 4…

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Q: 4 2. The volume of a sphere with radius r is given by V = (a) Take derivatives of both sides with…

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Q: If then f'(x) = f(x) = cos(sin(x)),

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Q: This question has several parts that must be completed sequentially. If you skip a part of the…

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Q: The demand for a new computer game can be modeled by p(x)=57-6 In x, for 0≤x≤ 800, where p(x) is the…

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Q: UPVOTE WILL BE GIVEN. PLEASE WRITE THE COMPLETE SOLUTIONS LEGIBLY. SOLVE IN 2 DECIMAL PLACES. BOX…

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Q: Suppose f(x) = 19x + 18e. Find: f'(2) = =

A: To find f'(2)

Q: A company purchases a blueprint plotter for $1500. The plotter cost for each set of blueprints is…

A: Let's assume that the total cost of producing 'x' sets of blueprints is C(x), where C(x) is a…

Q: Evaluate the integral. */6 1. sin³(x) dx cos(x)

A: See the details solution in below

Q: let y = x² +5, find dy/dx O none of these answers O 2x+5 2x O x²

A: Given query is to find derivative.

Q: Suppose f(x) = 7* log(x). Find: f'(x) = Note: Enter In(a) In(b) for log, (a).

A: Given query is to find the derivative.1

Q: 1) ɔ) Consider the region bounded by y = √x, the x-axis, and the line x = 1 as shown. Draw a…

A: see below the answer and explanation

Q: Given the following functions: f(x) = cos(x) and g(x) = x¹0 + 1. Find: f(g(x)) = 9(f(x)) =

A: f(x)=cosxg(x)=x10+1d dx(xn)=nxn-1d dx(cosx)=-sinxd dx(constant)=0

Q: f(x) = √√√x + 3 and g(x) = of 2: Find the formula for (gof)(x) and simplify your answer. Then find…

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Q: Write an equation for each graph.

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: Calculate the indicated limit. If the limit does not exist for any reason type DNE. lim 9(x² - x -…

A: Given query is find the limit.

Q: graph below to answers (and your 8- 6- pllowing question justitications!) in the space below. 2- 10…

A: We need to find differentiability.

Q: Determine where the function is (a) increasing: (b) decreasing, and (c) determine where relative…

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Q: Given the following functions: f(u) = tan(u) and g(x) = x³. Find: f(g(x)) = f'(u) = f'(g(x)) g'(x) =…

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