Verify that the conclusion of the Clairaut's Theorem holds a) z = sin(xy) b) z = sin(x - y) c) z = (1-x²)(1 - y²)

Q: The revenue (in dollars) from the sale of z infant car seats is given by R(x)=672-0.02², 0≤x≤ 3500.…

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Q: Lim. Zan² (4x) X² it: to x 70

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Q: Airlines sometimes overbook flights. Suppose that for a plane with 50 seats, 55 passengers have…

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Q: A thermometer is taken from a room where the temperature is 21°C to the outdoors, where the…

A: Newton's law of cooling is used.

Q: 8. Explain one difference in how & and 8 are used in the definition of limits. 9. For f(x) = 2x²,…

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Q: Rewrite the vector equation r(t) = (−4 − 3t)i + (3 − 2t)j + (−1 − 5t)k as the corresponding…

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Q: dx *√x2 - 1

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Q: 5) w(n) = -2n - 2; Find w(9)

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: For the pair of functions f(x) and g(x), find and fully simplify the following. f(x) = 3x - 15; g(x)…

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Q: plane region bounded above by the line y - 4. bounded below by the curvey-4-x.bounded on the left by…

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Q: Using the method you deem appropriate, solve the following equations and calculate the value of the…

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Q: The total number of births in an average woman's lifetime in Argentina can be approximated by the…

A: This is a problem related to function calculation. Please follow the procedure given below.

Q: A bucket is filled with sand so that the total mass (sand and bucket) is 10 kgs. The bucket is to be…

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Q: (4) If a point x is taken at random on the interval [0, 2a] and all the points are equally likely to…

A: Given :x2a-x>a22

Q: 1. Find the area of the surface generated by revolving the given curve about the x-axis. y=√4-x²…

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Q: 38. f(x) = = 1 3x - 2³ C=-1

A: We can solve it as follows for Taylor's series.

Q: What is the range of the given function ? x + 3, if x 3 O a. (-∞,0) U (2, + ∞ ) O b. (-∞ 8 0] U[2, +…

A: Given gx=x+3if  x<-3-9-x2 if  -3<x≤3x-1 if   x>3To find : Range of gxSolution :

Q: Is the differential equation y2dx + 2xydy =0 exact?

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Q: Find the solution set of the given equations/inequalities. Check for extraneous roots/solutions. 2x…

A: Given equation, 2x-12x-3-xx+1-2x+12x2-x-3=0

Q: For x > 0, the horizontal line y = 2 is an asymptote for the graph of the function f(x). Which of…

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Q: After t weeks of practice, a typing student can type 100(1e-0.5t) words per minute (wpm). How soon…

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Q: 1. (b) Find the exact numerical value of each expression cosh(-In 2)

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Q: Q / If you have th matrices S and M be the determinant of [₁ L60 55 48 M= 10] 14 43 10 /M*S/= S

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Q: 1 1-x ² dx

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Q: The function f is defined for all in the interval 3 < x < 6. Which of the following statements, if…

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Q: n=3 3n+ 5 n(n − 1)(n − 2)

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Q: 16. 8 n=1 1 (2n)!

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Q: Find an equation of the plane orthogonal to the line which passes through the point (9, 1, -10).…

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Q: f(x) = 6x-1 ax + b 8x-1 for x 1/1/201

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Q: dy/dx+y/x=xy^2 use y=v/x

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Q: Determine the linear function ?f knowing that the slope is 9 and ?(10)=18f(10)=18. ?(?)=f(x)=

A: The objective is to determine the linear function.

Q: Below are pie charts representing the U.S. voting age populations in 1960 and 2016¹ 1960 US Voting…

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Q: Determine the value of k such that y=4x²-3e²t is a solution to x(1-x)y"+ (2x²-1) y'+k(2x-1)y=0

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Q: Use the indicated substitution to evaluate the integral.

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Q: Sesin x cos x - acos 2x sin 2x)dx

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Q: Which of the following is the appropriate substitution for the Bernoulli differential equation xy' -…

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Q: 7) g(n) = 2n² - 4; Find g(-2)

A: Given: gn=2n2-4To find: g-2=?

Q: Find the first derivative of: i. (3x − 5)^-5

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Q: B -2 C -1 2 -1 O -1 -2+ Graph of f' Let f be a differentiable function with f(1) = -2. The graph of…

A: Given that a function f is differentiable and f(1)=-2.  Also the graph of first derivative of the…

Q: 1. Consider the IVP: y' = (1-2x)/y, y(1) = -2. (a) Use the method of Separation of Variables to…

A: To solve the initial value problem given.

Q: If a is a nozero real number, then lim (A) 0 B (c) 1 1 2a² D does not exist x²-a² x4-aª is

A: Use limit concept

Q: The curve y²-x²= -5x is a solution to the differential equation y'= (2x - 5)/2y A) FALSE B) TRUE

A: The answer is given below

Q: x² +1/x² = 34 , find the value of x⁴ + 1/x

A: Square the given expression

Q: x²y" + xy' = x² + y 2

A: See this solution in below.

Q: Find g'(x) if g(x) = logx(3x)2. 2 In x 3 In²x 8'(x)= 2 In 3 x In²x 2 In 3 x In²x 8'(x)=- 2 lnx 3…

A: You need to simplify the expression of g(x) first and then differentiate that.

Q: Given: + g(x)= x+3, if x3 What type of discontinuity occurs at x=3 ? O a. Jump Discontinuity O b.…

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Q: Find the set A UB. U= {1, 2, 3, 4, 5, 6, 7, 8, 9) A = {1, 2, 3, 5} B = {4, 1, 6} Select the correct…

A: To find the set A U B.

Q: Q4. Evaluate the following partial integrals: [₁21 -1 (a) (b) 2x - y dx r3x Love -x S dy xy dy

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Q: 13. == H

A: Radius of convergence of a power series is ∑anxn is given by 1R=limn→∞supan1n.Then interval of…

Q: length

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