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Q: Find an equation of the tangent plane to the surface at the given point. (2,0,0) g(x, y) = arctan…

A: Answer and explanation is given below...

Q: -1 Range of f -4 -5 -6 O (c) Describe the relationship between the graphs. Domain of 1 -81 Range of…

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Q: Which of the following graphs is the correct plot of y = 3 sin(x)? -4 3 2 1 -2 -5+ 5+ 1 2 3 4 O 6 3…

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Q: • У -ky = 19.2 2 + воё, усо) =ўс 4Х -ЧХ 4X Ans: Y = 22ë + +24xе X -Че

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Q: (b) Use Lagrange multipliers to find the maximum and minimum values of f subject to the given…

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Q: lim x→5 3x |x-5|

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Q: Find the inverse function (on the given interval, if specified) and graph both f and f graphs.…

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Q: Evaluate the following definite integral by using suitable trigonometry substitution: √2√3-2² dx.

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Q: 1 Give the antiderivatives of

A: The given function 1x2 we have to find its antiderivative

Q: Find the gradient of the function at the given point. g(x, y) = 12xe/x, (12, 0) Vg(12, 0) =

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Q: e) Find the linear approximation of the function f(x, y, z) = x³y² + z² at the point (2, 3, 4) and…

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Q: нх У - 169 = 19.2 ё + воё, усо) =ўс) 4Х 4X -4Х Ans: y=2.2 +e+24xe X - Че

A: Solution of given question is written in below steps.

Q: O O O O O IfE is the solid hemisphere a² + y² +2²5 49 and y 20, set up the integral using spherical…

A: Solution: In converting to spherical coordinates, we use so that

Q: ∞ Determine whether the series (-1)-In -1/3 is absolutely convergent, conditionally conver- n=1

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Q: Estimate the area under the graph f(x)=1/(x+3) Over the interval (-2,1) Using 8 approximating…

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Q: Find the domain of the function f(x) domain? = 1 √ x² + 1x 30 . What is the greatest value of a not…

A: The given function,  fx=1x2+x-30

Q: Write the given differential equation in the form L(y) = g(x), where L is a linear differential…

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Q: Find the area between the curves. 1/5 6/5 y=x, y = 4x ... The area between the curves is (Do not…

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Q: Prove that the graph of the function y = x² −3+1/x has at least two x-intercepts in (0,2).

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Q: Evaluate the following integral: dx So √1-x²

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Q: The father has just donated $25,000 to a church. His son would like to donate an equivalent amount,…

A: Given;  Principal =$ 25000 Time = 5 years  Rate = 8.2%.

Q: Use partial fractions to evaluate the following integral: x³ +6x²+3x+6 dx x³+2x²

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Q: y, 4e* In y, x = In (u cos v), y = u sin v; 4e* In (u, v) = (2, π/4) 7. z =

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Q: (b) Determine whether the series n=1 n 3n+2 n is convergent or divergent.

A: See this solution in below

Q: If cos x = 5/11 and the terminal point of x is in Quadrant IV, what is sin x

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Q: Write the given differential equation in the form L(y)- 90x), where L is a linear 4y"-15y4ys…

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Q: aU: Calculate the derivative of function is not differentiable at an explain in your own words why…

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Q: -4 -2 (a) x=¹t+3, y = 2² VX (b)x=²2t, y = √t 11 (c) x = ²³ - 2t, y = 2² - t ✓X III (d) x = cos(5t),…

A: Please see the below picture for detailed solution.

Q: Solve the initial value problem: y(x) = 2x - 4y√x² + 1. dy dx = 0, y(0) = -4

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

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Q: Find the radius of convergence and interval of convergence of the series n=1 (x - 5)n n5n

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Q: Evaluate the following limit or explain why it does not exist. 6 X lim (1+7x) X-0 Select the correct…

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Q: Find aw/as and aw/at using the appropriate Chain Rule. Function Values w = sin(2x + 3y) x = s+t,…

A: We can answer both the answer as below.

Q: Consider the differential equation x²y" - 6xy' +10y = 0; x², x5, (0, ∞). Verify that the given…

A: We need to find general solution.

Q: Find the arc length of the graph of the function over the indicated interval. (Round your answer to…

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Q: A white wine at room temperature 70° F is chilled in ice (32°F). If it takes 15 minutes for the wine…

A: Given that , Room Temperature T0=32°F

Q: 2. Determine whether or not the series converges. State clearly the test you use, and show all…

A: We have to check the convergence

Q: Sx tanx dx

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Q: If z=5x^2+y^2 and (x,y) changes from (1,2) to (1.05,2.1), compare the values of delta z and dz.

A: Given that        z=5x2+y2 changes from (1,2) to (1.05,2.1)  We have to derive value of Δz and dz .…

Q: Find the limit of the following sequence or determine that the limit does not exist. {n sin()}

A: Solve the following

Q: Without using a calculator, find the exact value of the expression: 20 cos(-315°) - 6 cot( - 135°).

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Q: From the point (5,12,13) on the surface of g(x, y) = √x² + y², find the direction of maximum…

A: The gradient vector is a vector made up of all the partials of a given function. We compute it by…

Q: 4. Solve y 3x 3y + 2y" e using undetermined coefficient. Show all the work.

A: We need to solve D.E.

Q: Find three positive integers x, y, and z that satisfy the given conditions. The sum is 33, and the…

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Q: Match the differential equations and the description/s that is/ are true to the differential…

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Q: 'y-1 ++ Beson Muss 1- +

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Q: 2 Solve the following ODES by 1.2 • ý -2y +y = e sinx Inverse Operator method X X Anse y=cie +…

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Q: Estimate the minimum number of subintervals needed to approximate the following integral with an…

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Q: I = √x f(x, y) dy dx-

A: ∫01∫0xf(x,y)dydx

Q: Find the derivative of the function using Chain Rule. (2x-6)-¹ (x²+3) h(x)=

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