Question 3: Suppose that H = xy + V3x2 + 4y?, and at t = 0 (initiation) we have r = 1, y = 1, H = 6, we have dx/dt = 1, dy/dt = -1. Approximately how much does H change in %3D %3D the first .01 seconds?

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A: Given thatrx=fghx where h1=5,g5=4,h'1=5,g'5=5,f'4=8 To find :r'1Solution:rx=fghxr'x=f'ghxg'hxh'xr'1=...

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A: To find the relative min or max of the given function. 

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A: We will find the partial derivative. 

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A: Since you have asked multiple question, we will solve the first question for you. If youwant any spe...

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Q: A mountain climber wants to climb up a mountain that is 1 000 meters high. In the first hour, he cli...

A: A mountain climber wants to climb up a mountain that is 1 000 meters high. In the first hour, he cli...

Q: 3. Determine whether or not each equation is a function. Justify your answers. a) y =- 2x + 5 b) x? ...

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Q: Vx+4 -3 3. Evaluatelim x-5 Show your complete x-5 solution.

A: topic - limits

Q: Use the graph of the function to answer each question. (-2n < x < 2n) f(x) = cot(x) 3 –27 2л

A: We have properties of cot function to solve this problem

Q: 24. Find the limit using the L'Hospital's Rule. a) lim x+0 (e2k-1) Inx b) lim X+0o x

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A: zeros is given 2, 3i, -3i

Q: O Use a linear approxi mation (differential) to estimate 3999

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Q: Solve ſ cot3 4x csc² 4x dx then evaluate the answer at x=22, C=26

A: ∫cot34x csc24x dx

Q: A. Fill in the table and guess the value of the limit. 1. lim f(x), where f(x) = %3D f(x) f(x) 1.002...

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A: Given:- A rancher with 750 ft of fencing wants to enclose a rectangular area and then divide it into...

Q: B. Find the value of the limit. 1. lim *+1)²(x-1) x1 x³+1 x²–4 2. lim x1 x2-3x+2 x²-4 3. lim x2 x-2

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Q: A company produces a special new type of TV. The company has fixed costs of $494,000, and it costs $...

A: NOTE: Refresh your page if you can't see any equations. . here fixed cost is $494000 and the variabl...

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A: Given query is to find perimeter of the triangle.

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Q: Find the the solution to the following system of equations using the Gauss-Jordan method: x - 2z = 0...

A: NOTE: Refresh your page if you can't see any equations. . system Ax=b is 

Q: Identify

A: We will solve the integration. 

Q: Determine whether the alternating series converges. 00 5ln k k k=3 O The series diverges. O The seri...

A: On solving this series we will get

Q: 7. If exactly 100 people will sign up for a local flight, the airline will change P 3,000.00 per per...

A: The given no. Of people is 100 and the charge is 3000 per person. If more than 100 people sign up, t...

Q: First make a substitution and then use integration by parts to evaluate the integral 6 cos (Vx) dx.

A: In this question we have to solve the integration.

Q: For the following composite function, find an inner function u = g(x) and an outer function y =f (u)...

A: topic - functions and derivatives

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Q: Use the graph of the function to answer the following. f(x) = cos(x) on the interval [-27, 2x] 2 -27...

A: Given that f(x)= cosx and in interval [-2π,2π]. We find increasing and decreasing interval and also ...

Q: dw If w = x2 + y2 and x = at?,y = 2at find dt

A: Differentiation

Q: x In(x) dx, where x >0

A: Given query is to eveluate the integral.

Q: Find and sketch the domain of z = f(x, y) = In(9 - x - y²).

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Q: On the graph of f(x) = cot x and the interval [27, 47), for what value of x does the graph cross the...

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Q: Write out the form of the partial fraction decomposition of the function: (x^4-2x^3+x^2+4x-1)/(x^2-2...

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Q: Find the derivative of the function. y'(x) =

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