An engineering firm recently estimated its total revenue function as TR = 300q - 6q2² and its total costs as TC = 4q².

Q: 1. Find the following antiderivatives. (a) [² cosh x + 1 sinhx dx

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Q: 1. f(x) = x² − 16x, [3, 10] 2. f(x) = 15 – 2x − 2x², [1, 2] 3. f(x) = 2x³ + 3x² − 12x + 24, [−4, 0]

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Q: Find  f(t). ℒ−1{1/(s - 7)3}

A: The inverse laplace tranform L-11s-73

Q: Determine whether the series converges, and if so find its sum. If the series diverges, indicate…

A: Above question is solved.

Q: A rectangle is enclosed by the coordinate axes and the line 2y + x - 5 = 0 Determine the length and…

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Q: se the Shell Method to compute the volume of the solid obtained by rotating the region above the…

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Q: Using implicit differentiation, find Provide your answer below: dy dx Content attribution dy dx √xy…

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Q: (1,2) (b) Set up a definite integral that is equal to the arc length of the portion of the circle…

A: Note:- As per your request i am solving here question no. 3 part B only.

Q: Find two positive numbers that satisfy the given requirements. The sum of the first number cubed and…

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Q: Solve the following D.E dy sin x- dx +2y = tan 2

A: Concept: First-order linear differentiation equation: The linear polynomial equation, which includes…

Q: 4. y" + y = 2xsinx

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Q: Evaluate lim 00 0-1/1/201 O None of the choices ¹ 0-1/201 O 14 tan z 1 x cos x

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Q: Write the first five terms of the sequence, give the exact answer: too n n+7 n=1 Determine whether…

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Q: hand written pl Let A(0,-2), B(0,4) (1) Find the set of all points P(x, y) such that m(PA) 2. m(PB)…

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Q: For the function R whose graph is shown, state the following. (If the limit is infinite, enter '' or…

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Q: 2. Consider the function F, that assigns x in its domain to x² - 1 F(x): |x-1| In its domain. a.…

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Q: For the function f whose graph is given, state the value of each quantity, if it exists. (If an…

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Q: Find F(s). ℒ{e−8t cos(6t)}

A: To find the laplace transform of the given function.

Q: J 6x x +3 dx

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Q: aximum profit is d to nearest integer.)

A: Topic:- application of derivatives

Q: 2. Determine the centroid of the area bounded by the curves y = 4x + 16, x = -2x = 5 and x-axis.

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Q: Let V be the volume of the solid obtained by rotating the region above the x-axis and below the…

A: Recall:  V=∫abπf(x)2dx We have a=0, b=6, f(x)=e-x

Q: + 75 3-4x Evaluate lim x-4 1 -4x-6 + Enter an exact answer. Provide your answer below: 13

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Q: 2. Evaluate the double integrals by iteration. whre B is the region 0 ≤ x ≤ 1, ² ≤ y ≤ = d.A

A: Let's evaluate given double integral.

Q: Deriving the formula for volume generated by revolving the first- 8x and the line x = 2 about =…

A: Given problem:- Deriving the formula for volume generated by revolving the first quadrant area…

Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

A: Let's solve given diffrential equation.

Q: Given f(x,y)= x³(x²y³-2y²), find all of the first and second partial derivatives.

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Q: Numeric Response 1. The Math Department is made up of ten math teachers, 4 male teachers and 6 fema…

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Q: dx (4x²-9)3/2 17.f

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Q: y sin(xy)dady csc²0d0dr ze-² drdydz (a) T/2 (5) [72² 1/2 π/2 ©fff (c) Jo Jo Jo

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Q: Evaluate the integral [e2 cos(2x)dx.

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Q: 2 1. f(x) = x² + 8x + 12 2 2. f(x) = x² + 25x 150 3. f(x) = x² + 18x130

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

Q: State the order of the given ordinary differential equation. (1-x)y" - 3xy' + 6y = cos x Determine…

A: Order = highest derivative order = 2

Q: Q5] Find Maclaurin's series f(x) = √² x

A: Use definition of maclaurin series

Q: . The region is bounded by X = y² and x = 4(y − 2)² Using horizontal rectangles, set – up the…

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Q: What value(s) of 8 are an appropriate choice when proving the following limit lim (4x - 2) = 6 x-2…

A: We have to find the epsilon delta method

Q: A 200-g sample of a radioctive substance is placed in a chamber to be tested. After 3 h, 140 g of…

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Q: f(x) = 45x6

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Q: Question 17 of 55 Compare 4 and -2. Which of the following is true? A. 141 -2 OB. 141-21 and 4 > -2…

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Q: ƒ(x) = x0.03 1 f(x) = X0.35

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Q: 1. Show that z³+y³ lim (x, y) (0,0) 1² + y² does not exist.

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Q: 2. Consider the function F, that assigns x in its domain to x² - 1 F(x) |x-1| In its domain. a. What…

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Q: Use the given graph of f to state the value of each quantity, if it exists. (If an answer does not…

A: Topic = Limits

Q: Question 1 If A = sin ui + cos uj + uk, B = cos ui - sin uj - 3k, and C = 2i + 3j - k, find (A X…

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Q: Determine whether the differential equation (7x² − 2xy + 2) dx + (8y² − x² + 7) dy = 0 s exact. If…

A: Topic:- differential equations

Q: Given the function f(x) = 4x + 3 Find the difference quotient Find f'(x) by determining lim h→0 Find…

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Q: 3) The correct solution of the center of mass bounded by x=y² and x= 2y = y² if the density is 6 = y…

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Q: What function do you know from calculus is such that its first derivative is itself? (Do not use the…

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Q: 11.f (4x+5)dx √√1-2x

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Q: Solve cos(x) = - 0.38 on 0 < x < 2π

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