2 Show that the total length of the astroid x¾ + y³ = a³, which can be parameterized as x = acos³0, y = asin³0, is 6a, where a is a nonzero constant. Hint: ds = (dx)² + (dy)² = √√/1 + (dy)²|dx|.

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A: See this solution in below.

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Q: How you recieve pi/4 in the first problem because when you put tan-1(1/2/12) = tan-1(1) and this is…

A: This is possible by the conversion of degree into radian.

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Q: =1 Find hat such that fal= (h ol F(x) = √x +13 -4 g(x) = 8x + Suppose that g(x) h(x) =

A: Topic:- calculus

Q: e. When is the greatest common factor of two numbers one of the two numbers? Explain your reasoning.

A: Given :   When is the greatest common factor of two numbers one of the two numbers

Q: The absolute maximum value is (Use a comma to separate answers at x = as needed.) The absolute…

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Q: Let where we don't know the base a. However, we do know that Use this information to compute L(x) =…

A: We have to find the values of given L(x).

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Q: C) f(x)=- --x-21-

A: Need to write down that how we can graph the given function and also need to find out the domain and…

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Q: Suppose that f(x) is a continuous function over all real numbers, f'(-16)=0, and f''(-16)=27 Which…

A: Given fx is a continuous function, f'-16=0 and f"-16=27

Q: Find the limits. f(x) = 2x² 3x + 15, g(x)=√x + 3 (a) lim_ f(x) = X-3 (b) lim g(x) = X→ 24 (c)…

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Q: Non-exact Differential Equations Verify that the following DEs are non-exact, then find the general…

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

Q: Show that the points A(8,-1,0), B(0, 1, 1), and C(2, 1, -3) are non-collinear.

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Q: g(x) = a sin²(x)+1 kx+1 2x+1 if x < if x ≥ π 22

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Q: Evaluate each of the following expressions using the given table of values. X f(x) g(x) (a) f(g(1))…

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Q: 1. Using Theorem 2.3.1 and Theorem 2.3.4, comput the derivative of the function g(x) = 16x² - 4x³…

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Q: Find y' if y= 48x³+34x2-8x+15 (4x-1)² 48x³+34x²-8x+33 (4x-1)² If y = 3u² - 2u + 4 and u = x² + 3x -…

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Q: If f(x)= log (8x), then f'(x) = If g(x) = (Inx)³, then g'(x) =

A: topic- derivative of a function we are givenf(x)=log(8x)g(x)=(ln x)3 and we know…

Q: FORMATTING: Write your answer in the form [p(x), q(x), r(x)], including square brackets and commas…

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Q: Solve 3xy + y + x²y² = 0

A: To solve 3xy'+y+x2y4=0 we can write its as 3xy'+y=-x2y4 or y'y4+y3xy4=-x23x which becomes…

Q: derivatives

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Q: traveling? 66. A patient placed on a restricted diet is allowed 1300 calories per day with a…

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Q: The curvature of a plane parametric curve x = f(t), y = g(t) is given by |x y - yx| [x² + y2]3/2…

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Q: C = {1,2,4,6} B = {3,5,7,9} 9 A = {1,2,4,6} f = {(1,3), (2,5), (4,7), (6,9)} g = {(5,6), (3,2),…

A: Given 1. A=1,2,4,6, B=3,5,7,9 and C=1,2,4,6 2. f:A→B and g:B→C 3. f=1,3,2,5,4,7,6,9 and…

Q: Can you answer question 5 please?

A: By change the f(x) and g(x) as polynomial we can change the value in different limit condition.

Q: Determine the solution xy³ dx + ye of the 1st Ordered Differential Equatio *dy = e*dy

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Q: Evaluate lim 1-cos3x x→0 tan 2x

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Q: iv. f/6(sec²(x)) dx

A: Integration

Q: 2 X +3X-4020 choose one Solution interval or D

A:

Q: 2-y If x = 32, find 2y 4. y+2 2y√ √2y B. dx B. Find y' if y = 4x-1 y-2 2y√ √2y (2x²-3)(3x+2)…

A: We can answer both the question in the below steps.

Q: 2. For the function h(x, y) = x+y², roughly sketch and label with their value the 7 level curves…

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Q: Researchers measured the average blood alcohol concentration C(t) of eight men starting one hour…

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Q: : | e³² Evaluate 3x e³x sin x dx.

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Q: ef= dx e + e- Evaluate

A: To evaluate the following integral.∫dxex+e-x

Q: The loudness, L, in decibels(dB), is given by the formula L = 10. log loud in decibels is this sound…

A: Topic- functions We are given,Loudnes L, in decibels(dB) by the formula L=10·logII0where I is the…

Q: 6. 7. 8. dy x- -= x² + y y = x² + 4x; dx In y = C₁e* + c₂e-x; yy" - (y')² = y² In y y−³ = x³ (3ex +…

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Q: Solve triangle ABC. (If an answer does not exist, enter DNE. Round your answers to one decimal…

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Q: express in form a + bi √-4 11

A: The given expression is -4 We have to solve the expression in the form a+bi

Q: 2 X₂ - 10X-4 = 0

A: To solve the following equation by using the method of completing the square.x2-10x-4=0

Q: 1 -dx Evaluate: J- 2 2 - 6x +8 +C |x-4 2 x-2 B. In|(x-4)(x-2) +C A. In 1, C. In x=2+C 2 X+4 D. In…

A: As per our guidelines we are supposed to answer only one question. Kindly re-post other question as…

Q: expand sin x/cos^2 x

A: expand sin x/cos^2 x

Q: x Find z. if z = xvey.x = rcos(t), v = rsin(t), when r = 2 and t =

A: Given; z=xyex/y, x=rcos(t), y=rsin(t)

Q: If f(x) = x+3 and g(x)=x²-2, find the following. a. f(g(0)) c. f(g(x)) b. g(f(0)) d. g(f(x))

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A: We need to find zx and zy.

Q: dy xẩy + y = xy3 dx

A: We are asked to solve the differential equations

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Q: Given f(x) = -2x² 18x - 36 x+6 Select the correct answer below: which of the following statements…

A: The given function is fx=-2x2-18x-36x+6 We have to check continuous at x=1

Q: (-8,-1) (-5,-3) (b) Let h be the function defined by h(x) (-2,1) = 1- g(x) x²+1 0 (1,5) Graph of g…

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