Consider the function FiR² -> IR given by f(x,y) := 3x² + 3y² for all (x, y) in 1² 2 fix an arbitrary point (a, b) € 1² prove f is locally linear or differentiable ar ab

Q: 3. Solve (x + y)dy = (x-y)dx x² + y² = c a. b. x² + 2xy + y² = c c. d. x²-2xy-y²=c x²-2xy + y² = c

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Q: 1. Assume that 1 mol of gas has the following equation of state: p = RT+b V. Answer the following…

A: as we know for gas equation that R and b is constant so variables are T and V p = RT + bV

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Q: For the parametric equations: = 24et and y = 144e24t (write the number answer only in the box) da dt…

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Q: Solve for a2f дхдz if f (x, y, z) = x³=3y

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Q: Let f(x) = x + ln(2 − x). - (a) Find the local linear approximation of f at xo = 1.

A: NOTE: Refresh your page if you can't see any equations. . substitute the given point x=1 which…

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Q: Given the differential equation y'=e^x/y and y(e)=1, what is C?

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Q: 7. Given a DE: y" + 2y' - 8y = 0 and a solution of the form y = ex for some (unknown) constant "r".…

A: The objective is to solve the above question.

Q: Elementary Differential Equations (Upvote will be given. Please write the complete solutions…

A: Let's solve given differential equation.

Q: Evaluate the following integral,     ∫     ∫   S z dS, where S is the part of the sphere x2 + y2 +…

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Q: 2. Find all vertical and horizontal asymptotes to the graph of f(x) Justify your answer. = 1 (x -…

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Q: Find integral 21 P=5 Sin (2x x3 x 10³ It dt- 3

A: To evaluate the following integral.P=5∫02πsin22π×3×103t dt

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Q: I cannot understand what you wrote unfortunately

A: NOTE: Refresh your page if you can't see any equations. . first, we need to simplify the given…

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A: To determine the characteristics of given differential equation

Q: 3. S sec² x tan² x+4 dx

A: dtanxdx=sec2x∫1a2+x2dx=1atan-1(xa)+c

Q: x²(1-x) dx = ['₁*²₁₁ - = 0 [² x(1-x)²dx

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Q: The City Council proposed to utilize government-owned land with an area of 21,600 square meters.…

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Q: (D²+ 3D-4) cos 2x

A: To evaluate the particular integral of given differential equation

Q: Express the integral as a limit of Riemann sums using right endpoints. Do not evaluate the limit. [°…

A: To express the integral as a limit of Riemann sums by using right endpoints.∫466+x2 dx

Q: 4 1. Evaluate f √₁²₁ √1 + xª dx.

A: we will find the required.

Q: ind the slope in the x-direction at the at P(0, 2, ƒ(0, 2)) on the graph of f when f(x, y) slope = 0…

A: We will find the required.

Q: Evaluate fyxz (1,2,0) for f(x, y, z) = 9x²z - e²x-y

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Q: Find the slope of the line tangent to the polar curve at the given point. 9 5x 26 r=9 sin 0; dy Find…

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Q: Plot the points with polar coordinates (-5, 2¹) and 3, π 5л 6 71 6 3μ 4 5π 4 2л 3 41 3 EIN π 2 3μ 2…

A: We need to mark given coordinates.

Q: Estimate the value of log,8.9. O 2- 2+ 2+ 1 90 1 60 ✔ logge -logge - 108 90 1 2- - logge 60

A: The objective of the question is choose the correct option by evaluating.

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Q: The final should be 4 no? Not 23/6?

A: Given Vector:- F→x,y,z=lnx+y+xzπ,1+yzsinhy,zey-cosz

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Q: Select the graph for which f¹(x) > 0 a) b) c) d) v r and f(x) > 0

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Q: Use Gauss-Jordan elimination to solve the system 5x + 7y = −11 2x + y = 1 Make sure you create…

A: The given system of equation is  5x+7=-112x+y=1 We have to solve the system using the Gauss-Jordan…

Q: plicit differentiation ex sinz-zlnx + ey arccos(22) = 0 ; дz S/8

A: Given query is to find indicated partial derivative.

Q: 5) Find, using Cylindrical Coordinates, the volume of the solid that is enclosed by the cone and the…

A: Cylindrical coordinate

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Q: Which of the following statements are true: A. in 3-space the intersection of the graphs of is a…

A: We have to find true statements from given options.

Q: Find the volume of the solid in R3R3 bounded by y=x2y=x2, x=y2x=y2, z=x+y+15z=x+y+15, and z=0z=0

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Q: What is the value of k in the ANSWER: k = Blank 1 Blank 1 Add your answer equation (7² - - 3e)dx =…

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Q: The polynomial of degree 4, P(x), has a root of multiplicity 2 at a x = 0 and x = - 1. It goes…

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Q: get the homogenous solution then solve after getting the new equation xy' = y(lnx-lny), y(1) = 4

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Q: List the first five terms of the sequence. a1 a2 23 a4 25 = = = = = a₁ = 18, an+1 = n

A: given a1 = 18 an+1 = ann

Q: Consider the function F(x) = fx et dt. Find F'(x): Check F'(x) =

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Q: Let f(x) = x + ln(2 − x). (a) Find the local linear approximation of f at xo = 1.

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