1. Find the maximum value of f(x, y, z) = x + y − z subject to the constraint x² + y² + z² = 6.

Q: If My - N N equation = Q, where is a function of a only, then the differential has an integrating…

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Q: If an> 0 and Σ an converges, then Σ(-1)"an converges.

A: We have to check wheather it is true or not

Q: For the function f(x)=ln(1−5x)​, find the Taylor polynomials of orders​ 0, 1,​ 2, and 3 generated by…

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Q: Find an equation for the conic that satisfies the given conditions. ellipse, center (-1, 3), vertex…

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Q: Let f be a function defined for t 2 0. Then the integral {f(t)} =[e-stf(t) dt is said to be the…

A: We need to find Laplace.

Q: Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s.) f(t) = (et-e-t)² L{f(t)}…

A: Given function f(t)=(et-e-t)2  f(t)=e2t+e-2t-2×et×e-tf(t)=e2t+e-2t-2   Formula L(eat)=1s-aL(c)=cs

Q: Use Definition 7.1.1. Definition 7.1.1 Laplace Transform Let f be a function defined for t≥ 0. Then…

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Q: What is the directional derivative of f(x,y,z) = ln(x²+2y²+ 4z²) at the point P(-1, 2, 4) in the…

A: The given function is; f(x,y,z)=ln(x2+2y2+4z2) Point P(-1,2,4) u=-3i/13 -4j/13 -12k/13.

Q: Differentiate y = (2x³ + 3x² - 1)5 30x(x + 1)(2x³ + 3x² - 1) O 5(6x² + 6x)+ 30x(x+1)(2x³ + 3x² - 1)4…

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Q: Set up an integral with appropriate limits for the average value of the function, f(x, y) over a…

A: Solution: y =|x| Let : f(x) = |x| The average value of a function favg Because f(x) and favg bounded…

Q: (x-2y) dx + (2x+y) dy = 0 Prove that it is a Homogenous DE using homegeneity test (degree n) and…

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Q: Find an equation of the tangent line to the graph of the function at the given point. y = 8x…

A: Given: y=8x arccos(x-1) and point (1,4π)

Q: Find the Taylor series generated by f at x=a. f(x) = 5x , a = 7

A: We have to find Taylor series of f(x) =5x about x=7. Let us see first what is Taylor series…

Q: area is given by the function x^0.5+y^0.5=1

A: We have to find the area of given function.

Q: 20 29t2 +42t represents the position function for a particle moving The function s(t) = along a line…

A: The given function is: s(t)=203t3-29t2+42t  where t∈0, 6 v(t)=d(s(t))dt=d203t3-29t2+42tdt=20t2…

Q: 12. Find an equation of the line tangent to the curve at the point corresponding to the given value…

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Q: Solve the given Bernoulli equation by using this substitution. O O O y = ± y = ± y = ± y = ± y = ±…

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Q: Use linear approximation, i.e. the tangent line, to approximate √81.1 as follows: Let f(x)=√√x. Find…

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Q: Let y 3x². Find the change in y, Ay when x = = 4 and Ax = : 0.2 Comm Find the differential dy when x…

A: We have to solve given Questions.

Q: Ľv 3x² - 2x + 3. (3x - 1). dx O -4.87 -3.92 -2.22 O -1.67

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Q: Solve the differential equation y'=1+5y subject to the initial condition y(0)=1. From your solution,…

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Q: Find the differential equation of the family of circles with centers on the line x – 2y = 3 and…

A: Given:  circles with centers on the line x – 2y = 3and passing through (3, 0).

Q: Let y Ay - 5x² + 8x + 4. If Ax = 0.4 at x = 5, use linear approximation to estimate Ay I Submit…

A: We know that ∆y=f(x+∆x)-f(x). So,             ∆y=f(x+∆x)-f(x)      =f(5+0.4)-f(5)      =5·…

Q: Sketch a graph of the polar equation. 3 2+3 cos 0

A: The given polar curve r=32cosθ

Q: 35. Choose the integral which represents the area between two curves given on the picture. 2- 1…

A: To choose the integral which represents the area between two curves given on the picture.

Q: etermine whether the equation is exact. If it is exact, find the solution. 2e³ycosy + 1² С 2e¹ycosy-…

A: We have to find solutions

Q: n-1 3n-1 Determine whether the series Σ=1 is convergent or divergent. If it is convergent, find its…

A: Using Cauchy criteria find that series is divergent

Q: In each part, use the given information to find A. (7A)-1 (b) (7A) -3 [] -2 = (d) (/+2A)-! = 2 4 5

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Q: The half-life of Radon-222 is 3.8 days. A 34-gram sample of Radon-222 is monitored for one day. How…

A: Please see the below picture for detailed solution.

Q: Which are the foci for the hyperbola modeled by the equation (Y-32 (x-1)² _ -1? 36 13

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Q: Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat…

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Q: For an arithmetic sequence, a17 a1 = the sum of the first 65 terms= > Next Question - 47. If the…

A: It is given that, a17=47 and common difference(d)=5 a1=? Sum of the first 65 terms=?

Q: Find the limit. lim (x,y) → (1,−4) 3x²y 2 1+xy²

A: I am attaching image so that you understand each and every step.

Q: the answer is wrong

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Q: Which of the following is the equation of the ellipse with a vertical major axis, center at (1, -3),…

A: Here we have to find the equation of an ellipse.

Q: 6. Find the y" + y = sec³ x; y(0) = 1, y'(0) = 1. -√2 value (7) for a solution (x) to the initial…

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Q: Use the triangles given on the right to evaluate the expression given below. If necessary, express…

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Q: At noon, ship A was 16 nautical miles due north of ship B. Ship A was sailing south at 16 knots…

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Q: Given f''(x)= Find f ƒ(7) = = 1 25 sin(5x) and f'(0) = 5 and f(0) = -6.

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Q: Answer true or false. If L{f(t)} = F(s) and L{g(t)} = G(s), then ¹{F(s)G(s))} = f(t)g(t). True False

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Q: 2. The table shows values of the function y = G(t). Use the table to estimate the value of 50…

A: Physical significance of integration is calculation of area under the curve. Here discrete values at…

Q: II. Consider the function f(x, y) defined for all (x, y) by ƒ(x, y) = 232/32 + 2xy + 4x²y (a) Find…

A: Here we have to find the critical points.

Q: Let f(x) = |x-1 (a) Make tables of the values of f at values of x that approach x = -1 from above…

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Q: An automobile company is ready to introduce a new line of cars through a national sales campaign.…

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Q: Question 9 of 20 View Policies Show Attempt History Your Answer Correct Answer Correct. Solve the…

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Q: Answer the following questions for the function f(x)=x√√x² +9 defined on the interval -7 ≤ x ≤ 4.…

A: Concept: Concavity: Assume that f(x) is differentiable on interval I. If f′(x) is growing, the f(x)…

Q: The formula for the volume of a cone is given below. Find the rate of change of the volume for each…

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Q: Find the first derivative of ƒ(x) = 7x¹⁰² cot(x). 10 f'(x) =

A: Given :fx=7x10excotx

Q: If r(t) = (e³t, e-4t, t), find r'(0), T(0), r"(0), and r'(0) x r"(0). r'(0) = II T(0) = r"(0) =…

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Q: Find the domain of the vector-valued function given below. r(t) = √√16-t²i+ 1 t+6 j+(t−4)k

A: We have to find the domain of the vector-valued function rt = 16-t2i + 1t+6j + t-4k