Find Duf at P. f(x, y, z) = 6x²y³z¹; P(1, −2, 2); u = 1+ 2 3 k

Q: 9) /(x) = 3 · -8 -6 -4 -2 | x + 1 20 18 14 1 12 10 8 ଣ 4 + 2 2 4 6 X

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Q: EXAMPLE 2 Prove the following limit. lim 5x - 6 = 14 SOLUTION 1. Preliminary analysis of the problem…

A: we need to find the value of δ such that the given limit is satisfied for any chosen ε.

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Q: The cost c in terms of the quantities 9₁ and 92 produced of good 1 and good 2 is given by c = 200 +…

A: differential

Q: Consider the following graph. y -5 4 3 2 (x, y) = 1 (x, y) = 1 2 3 4 5 6 (a) Find the interval(s) on…

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Q: 4. Given 1 = f(x,y) dydx + f(x,y) dydx, do the following. (a). Sketch the graph of the region of…

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Q: evaluate to dx dx integral 540

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Q: Find the most general antiderivative. (Use C for the constant of integration. Remember to use…

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Q: The population (in millions) of a country in 2007 and the expected continuous annual rate of change…

A: Given : k= - 0.006 P(7) = 2.3

Q: How long, rounded up to the nearest year, will it take me to become a millionaire if I invest $3,000…

A: Given data Principle, P= $ 3000 Interest rate, R = 12 % Time in years = t Amount, A = $ 10,00,000

Q: dy Compute if dx y = = (e²+7³) cosh5 (ln x) (π + e)e²+ cot-¹(5x²)

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Q: Find the directional derivative of f at P in the direction of a. f(x, y) = 3 tan ¹(²); P(-4,4);…

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Q: Use Taylor series expansion of an appropriate function to prove the following equalities: (a) (b)…

A: The solution is shown below-

Q: a(t) = 5i + 8k v(0) = 8j, r(0) = 0

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Q: K Estimate the volume of material in a cylindrical shell with length 46 in., radius 9 in., and shell…

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Q: A company manufactures and sells x television sets per month. The monthly cost and price-demand…

A: we need to find out the maximum revenue, maximum profit,

Q: 39. y = x + x=1 (x > 0)

A: We can solve the given problem by using the first derivative test.

Q: Find parametric equations for the line whose vector equation is given. (a) (x, y) = (6,-4) + t(1,-4)…

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Q: 2. Rewrite the integral f(x, y, z)dzdxdy using the order dxdydz.

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Q: Next Find the volume of the solid bounded by the paraboloids z = −6+3x² + 3y² and z = 7 - 2x² – 2y²

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Q: Exercises In Exercises 1-8, find a point c satisfying the conclusion of the MVT for the given…

A: As we know from the Mean value theorem: If the function fx is real-valued function is defined on a,b…

Q: Determine the dimensions of the rectangle of largest area that can be inscribed in the right…

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Q: Year 1950 1960 1970 1980 1990 Rate of change (million people per year) 27 42 59 79 96…

A: Given that , Year 1950 1960 1970 1980 1990 Rate of change (million people per year) 27 42 59 79…

Q: 6. If f(1) = 10 and f'(x) ≥ 2 for 1 ≤ x ≤ 4, how small can f(4) possibly be? Hint: Apply the Mean…

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Q: If the series is convergent, use the Alternating Series Estimation Theorem to determine how many…

A: We need to find the number of terms as per given condition.

Q: Q1:What is the limit of Riemann Sums as the number of rectangles (N) increases toward infinity?

A: Solution: As the number of rectangles (N) in a Riemann sum increases toward infinity, the…

Q: What is the equation of the verti asymptote of the following grap

A: here , we have graph of a function , then we have to find equation of vertical asymptotes :-

Q: г. у = эу! 3 X+l 3 y² = (x+₁).0 - 3 [1] (x+1)² ) - X - 3 (x+1)² + (x-1)0-3[1] (x-1)² (Aus) 3 (x-1)²

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Q: Evaluate each of the following indefinite integrals.  ∫e2xsin3xdx

A: Answer is in step 2.

Q: 8. farmer with 750 feet of fencing wants to enclose a rectangular area and then divide it into four…

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Q: 7x If h(x) = (1 + 4)¹x, find lim h(x) X→∞

A: In the question is :h(x)=1+4x7xlimx→∞hx=limx→∞1+4x7x

Q: 3. If lim[x² -f(x)] = 2, use the Rules of Limits to evaluate lim x-

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Q: Y=√x /n(x)

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Q: Order the functions by growth rate. a(x) = 85x c(x) = = x log₂ (x) + 5x! Select function ✓ Check…

A: In this question, we want to order the functions by growth rate. The given functions are-…

Q: (Draw your own grid):

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Q: Find y' and y". y' y" 11 = y = ( 2 + √x) ³ 3

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Q: n k=1 (3 + 2k)² = Hint: Start by multiplying out (3 + 2k)². fra

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Q: For the limit lim, (x3 - 3x + 2) = 20 3 illustrate the definition by finding the largest possible…

A: We have to find the largest possible values of δ.

Q: Evaluate the following integrals and/or determine whether the integral is convergent or divergent…

A: Note:- Since you asked multiple question, as per policy we can solve only first question for you…

Q: Find any relative extrema of the function. List each extremum along with the x-value at which it…

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Q: (Q1.) State whether the following equations is linear or non-linear and gives its order, degree, and…

A: Solution is given below:

Q: Σ1/(In(n))^4 [1/(n(In(n))^4) [(n+1)/(n^{3/2}+n) Σ1/(3^n-5) sin(n)/(3^n) 1/(n^5 -1) (4) (6) Direct…

A: The solution is shown below-

Q: In the article "Do Dogs Know Calculus?" the author Timothy Pennings explained how he noticed that…

A: Let DC be x and  t(x) represents time taken by the dog, Elvis in travelling  the distance AD at the…

Q: Find the absolute minimum and absolute maximum values of f on the given interval. f(x) = (x² − 1)³,…

A: f(x) = (x2 - 1)3 Interval = [-1 , 5]

Q: Determine the area of the triangle shown below using your knowledge of vector (-4,2) B A(3,5) 1718-8

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Q: Solve the given system of differential equations by systematic elimination. D²y = e4t Dx + (D+1)x+…

A: The given system is:Dx+D2y=e4t                                .... (1)(D+1)x+(D-1)y=2e4t…

Q: dx 3 Assume that x = x(t) and y = y(t). Let y = x³ +3 and=5 when x = 1. dt dy Find when x = 1. dt dy…

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Q: Find the Taylor polynomial P3(x, y) of degree three of the function f(x, y) = sin(xe") at the point…

A: Given function:- fx,y=sinxey

Q: Give an example of a:) two independent events and b.) two dependent events.

A: Event: An event refers to a specific outcome or occurrence that can happen in a particular situation…

Q: ∞ 3" Σ n=12" + n

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