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Q: . Given TR = 45Q -0.5 Q², TC = Q³-8Q² + 57Q + 2, find out the level of : output at which firm…

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Q: Sketch the region enclosed by y = ¹, y = e, and x = 1. Find the area of the region.

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Q: 2 1. The area of a rectangle is represented by the function A = 12x² + 48x + 48 cm² What is the…

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Q: 3. 2 csc 2x = sec x csc x

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Q: MATH401 Question 3|- functions and numbers A. Prove that cos-¹(-x) = π cos-¹(x) for any real number…

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Q: Evaluate the limit of the given functions. 3x17x+ 20 lim. x44x² 25x+36 1. 2. lim t3 - 1 고 t-it-1

A: "According to the guidelines issued by the company we are supposed to answer only first three…

Q: 1. The graph of y = f(x) is given below. -4 2 2 a) Find lim f(x) or state why it does not exist. 7+1…

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Q: B.Verify if a given function is a solution to a differential equation. 1 d²y dy 1x². +x=y= ln x dx²…

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Q: Answer the following True or False. 1 COS T dz = ln(cos z) +C

A: Our Aim is to answer whether the value of integral obtained is true or false.Given integral…

Q: 20. A store finds that its sales revenue changes at a rate given by S'(x)=-3x² +300x dollars per…

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Q: If f(x) = (t + 3)e' dt, on what interval is f increasing? (Justify your answer)

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Q: Answer the following True or False. If g(x) is a continuous function and h(x) is differentiable such…

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Q: 1. Use the Mean Value theorem to show that for any two real numbers a and b, we have | sin b - sin a…

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Q: Evaluate the indefinite integral. 4 (t + 4)³ dt + C

A: Topic = Integration

Q: A diabetes test is positive 85% of the time when the patient has diabetes and negative 95% of the…

A: Given data:- Diabetes test is positive 85% of the time when the patient has diabetes  diabetes test…

Q: Find the values of x, y and z that correspond to the critical point of the function 2 = f(x, y) =…

A: The given function fx,y=4x2+8x+7y+3y2 To find the critical points of the function

Q: Evaluate the triple integral W z dV where E is the solid bounded by the cylinder y² + z² = 100 and…

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Q: Assume that the shape of the athlete's high-jump is parabolic. the function, in vertex form, where…

A: The axis of symmetry is t = 0.6 and the maximum height is 1.80 mhence the vertex is  (0.6, 1.80)

Q: dr Let A be the area of a circle with radius r. If dt = 2, find dA dt when r = 4.

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Q: The opposite vector of 10 N [S80°W] is 10 N [W10°S]. True False

A: Please see the below picture for detailed solution.

Q: The graph of f(x) is shown (see figure). 2X f(x) = (a) Find the following limits. L = lim f(x) = V…

A: According to guidelines, we must answer only three of the multiple subparts given. So, I answered…

Q: 8. A trapezoid has its vertices at (0,0),(a,h), (a + b1, h), (b2,0), with all the letters denoting…

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Q: Find the generated volume f(x)=sin(x) and the lines x=0 and x=π and rotate about the x-axis V=π^2…

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Q: 10. (a) m = 0 L₂ (b) m = -² L₁ (c) m = 1 L3

A: Here, the given lines are with the slopes m=0m=-34m=1

Q: Question 6 Determine the Fourier series for the function defined below: f(x) = 2x in the range x = 0…

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Q: Which of the following is the complete set of roots of the auxiliary equation fory"'' - 3y "' + 3y…

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Q: Det er mine absolutely it each convergent, Conditionally convergent, you > k=1 the following is or…

A: Given ∑k=1∞coskπk

Q: 2 √9x²-16 x² dx

A: We will use substitute method to solve the integration

Q: A solution of the differential equation d²y dy +4- + 4y = 4e¯¹ dr2 da takes the value 1 when z = 0…

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Q: TU 2. fz sin² x cos4 x dx J

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Q: Which of the following functions will have a dashed line for the graph? y ≤ 4x^2 + 1 y = 4x^2 + 1…

A: Question : Which of the following functions will have a dashed line for the graph? 1. y ≤ 4x^2 + 1…

Q: 1. A 6 kg sign is suspended by two strings making angles with the ceiling as shown in the diagram.…

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Q: 2. a. b. C. f(0) = lim f(x)= x-0+ lim f(x) =

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Q: Find the direction vector of the line which is the intersection of the planes x + y + z = 1 and…

A: I am attaching image so that you understand each and every step.

Q: 16. Given the graph of g(x), Draw the graph of g-¹(x). Show your strategy for drawing the graph of…

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Q: 1. Find the area under one arch of the curve y = cos- :cosex.

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Q: The volume of the box is 54 cubic inches. The material for the top cost $0.08 per square inch, for…

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Q: 8. Give examples of sets of three vectors that are a. Collinear b. Coplanar c. Not coplanar Explain…

A: Solution: a) Collinear : Two or more vectors are called collinear when they are parallel to the same…

Q: = Set up the definite integral required to find the area of the region between the graph of y y = 2x…

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Q: - 7. Find the area bounded by the curve y² + x − 4y = 5 and the y — axis

A: We have to find the area of the given curve and line.

Q: 3.2 Bus A leaves Worcester at 08:00 and travels north along the N1 at 50 km/h. Bus B leaves…

A: Given that The Bus A leaves at 8:00 with speed of 50 km/hand bus B leaves at 10:00 with 70 km/hSo,…

Q: 1. (a) Use the Euclidean Algorithm to find ged(125, 793). (b) Using the workings in (a), find m, n €…

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Q: Let R be the region enclosed between the curves r²=y-1 and y=5. Sketch R and find its area.

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Q: 4. The population, P, of a school of fish t years after being released in a new habitat is given by…

A: The solution is given below

Q: Find a power series representation for the function. (Give your power series representation centered…

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Q: 10 times as many as 1 hundred is_______ hundreds or ________ thousand

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Q: Consider the function f(x) = x² + 2x - 8 x - 3 a. Find the first derivative. f'(x) b. List any…

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Q: Below is the function f(x)., 17+ 6 5 4 3 2 7 -7 -6 -5 -4 -3/-2 -7 -7 -2 -3 -4 -6 71 1 2 3 4 5 6 7…

A: Please see the below picture for detailed solution.

Q: e) fx³ √2x² +1 dx wil(-) {. ub f CP

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Q: The shaded region between the graphs of y x I I - 2x² + 20 and y = 3x - 15 is displayed below in 25…

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