Question Find the area, in square units, of the region bounded on the left by the line g(x) = 2x + 10, on the right by the parabola f(x) = -(x - 1)² + 36, and below by the x-axis by integrating with respect to y. Do not include units in your answer.

Q: Book Problem 31 Find a function f and a positive number a such that f(x): a = = + [² 2+ f(t) dt =…

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Q: Book Problem 19 (a) Find the average value of f(x) = 25 - x² on the interval [0, 5]. Answer: (b)…

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Q: Use the chain rule to help you find dy/dx for each of the following functions: 10. y = (x²+4)³ 12. y…

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Q: Find the inverse function of f. f(x): = -64, X>0

A: To find the inverse of a function f(x) : Rewrite f(x) as y Switch x and y  Solve for y

Q: If your weekly cost, C, (in dollars) to manufacture L laptops and D desktops is: C(L, D)= 5000+50L…

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Q: Suppose f(x) and f'(x) have the following values. I 5 6 7 8 9 f(x) 14 18 8 6 11 f'(x) -3 7 -10 -9 2

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Q: 7 ♡ Ņ T 2 0 -1 -2 y-intercept x-intercept Return this question to its initial state 3₂2 Drag the…

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Q: 1. (Difference Quotient) Simplify the difference quotient (x+h)-f(x) for each of the following…

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Q: a tractor is purchased by a local farmer for $ 12,000 and straight - line depreciates to $ 0 in 20…

A: Given 1. Purchase price of tractor =$12,000 2. Depreciates to $0 in 20 years

Q: (3) Find the radius of convergence of a) infinite b) 1 not defined 0 infinite X Σ₁ F

A: The given series is: ∑j=1∞xjj2 Let, aj=xjj2; j≥1

Q: Find the set on which the curve is concave upward. Answer (in interval notation): | 2 y = ₁² 1²+ 3²…

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Q: Hello good people, how are you, I need you to write these numbers in polar form for the complex in:…

A: Note that, if z=a+ib then z=reiθ=r(cos θ+i sin θ) where r=a2+b2 and θ=tan-1ba

Q: Determine the area, in square units, of the region bounded by f(x) = 10x³ + x² - 21x - 9 an g(x) =…

A: To determine the area, in square units, of the region bounded by fx=10x3+x2-21x-9 and gx=9x3+x2-5x-9…

Q: 0.602x(3×3!/4)=? (Gamma function)

A: This question can be solved using the formulas related to gamma function

Q: Show that the equation represents a circle by rewriting it in standard form. x² + y² - 6x + 6y + 2 =…

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Q: The energy expenditure (in kcal/km) for animals swimming at the surface of the water is given by y =…

A: The energy expenditure (in kcal/km) for animals swimming at the surface of the water is given by…

Q: Simplify [cos 20-i sin2018[cos 30+ i sin301² [cos 40+ i sin40 1³ [cos 20-i sin2015 using De Moivre's…

A: This question can be solved using the De Moivre's theorem which says eix=cosx+isinx

Q: 5.Find each of the following limits if they exist. A. lim x-11 B. lim x-1+ TH

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Q: Let 9-- 9 4 Part A: What is a coterminal angle of such that 0 ≤ 0≤2m? Part B: What are the exact…

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Q: Question Find the area of the region pictured below that is bounded by the functions u(y): the area…

A: The region is bounded by the curves u(y)=y-3 and v(y)=y2-2y-13 on the interval -2≤y≤5 use the…

Q: Consider the function f(x) = 4x + 2. (a) Estimate the area between the graph of f and the x-axis…

A: given f(x)=4x+2a=0 to b=3n=6 (no. of rectangles)Δx=b-anΔx=3-06=12

Q: a) f(x,y) = x³y² + 6xy b) g(x,y)= 6x-x²-8y-2y²

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Q: X Given zx 2cos u; y = 3sin v, find y O-2cos u cos v 3 sin ² v O 2sin v 3 sin u O-2sin u 3 sin v…

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Q: Q4. Choose two of the following: (a). If x = t - t² and y = t-t³. Find 2 by using Chain Rule. dx²…

A: a) x=t-t2 and y=t-t3 b) fx=1+x at x=3 c) fx=2a+x2,x≥12x+b,x<1 is continuous at x=1and f-1=5 Use…

Q: 1. Sketch the graph of the equation. x2 + y2 + 10x − 4y + 29 = 0   2. Complete the graph using the…

A: Given problems:- 1. Sketch the graph of the equation. x2 + y2 + 10x − 4y + 29 = 0 2. Complete the…

Q: 3. Consider the initial value problem (IVP): ty' — y = t²e-t, y(1) = −1. (a) Use integrating factor…

A: We will use integrating factor method to solve this.

Q: Determine using Cauchy Riemann equations the function below is analytic or not in z-plane? f(z) = x…

A: See the details solution in below

Q: Write ftan¹¹ 11x dx in terms of ftan" a da 4

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Q: Q5. Find a general solution for the following second order non homogenous ODES. y"-4y' + 4y = 2e²x +…

A: Given: y''-4y'+4y=2e2x+4x-12 So, we can also write as; D2-4D+4y=2e2x+4x-12 The auxiliary equation…

Q: 1. If y=tanx, prove that y=2(y² +1)(3y² +1).

A: y =tanx y'''=2(y2+1)(3y2+1).

Q: 22 e 1-§ 2(2-21) ² c: |z_11 = 1/2, 17-11-2

A: The given integral I=∮Ce2zzz-2i2   ;  C=z-i=12, z-i=2 Cauchy integral formula:   suppose that C is…

Q: Find median and mode of the messages received on 9 consecutive days 15, 11, 9, 5, 18, 4, 15, 13, 17.…

A: Please check the given options because the answer to the given question is not among the given…

Q: Use the graph to find the following limits. a. lim f(x) X-1 b. lim f(x) X-3 a. Find lim f(x) or…

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Q: (c) If b = 1, what is the range of this function? (Enter your answer using interval notation.)

A: Topic = Function

Q: How do you simplify eiπ?

A: To find the value of eiπ   Formula:   By Euler's formula: eix = cos x +i sin x

Q: Book Problem 24 If F(x) = f(t)dt, where f(t) = Stº F"(x) = Note: You gon I √7+u² U du, find: and F"…

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Q: 7. f is a differentiable function on the interval [0, 1] and g(x) = f(4x). The table below gives…

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Q: Find the following limit. 2 lim h→0 √2h+1 +1

A: Limit

Q: [ 0 y-y² y-y² (y - y² - x²) dxdy

A: Given equation: ∫01∫-y-y2y-y2(y-y2-x2) dx dy

Q: Find the limit. (If an answer does not exist, enter DNE.) 4(x + Ax) - 4x Ax lim Ax-0 I

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Q: H

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Q: Rewrite the differential equation as. dy y(x+2)-(x+2) dx y(x-3)+(x-3) = (x+2)(y-1) (x-3)(y+1) dx (1)…

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Q: If the coordinates of any two points ₁ and ₂ are (x₁, y₁) and (x2, ₂), respectively, then prove that…

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Q: 1) GIVEN: FID: X, 9, X 9 3

A: Disclaimer:  “Since you have asked multiple question, we will solve the first question for you. If…

Q: A piece of rectangular sheet metal is 24 inches wide. It is to be made into a drain gutter by…

A: We have to find the value of x that gives greatest capacity.

Q: How many distinct permutations can be made from the letters of the word "miscellaneous" that start…

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Q: 1. The graph of f '(x) is continuous and increasing with an x-intercept at x = 4. Which of the…

A: Let's solve.

Q: Find Domain and Range y=- ex-1 The domain is (-00,00) and range is (-00,0) The domain is (0,00) and…

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Q: Find an equation for the function f that has the given derivative and whose graph passes through the…

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Q: Question Find the area bounded by f(x) = x³ + 3x and g(x) = 4x on x € [−1, 1]. Submit your answer in…

A: The area between the curve is given by ∬dydx.see below the answer and calculation