Question 2 A₁ 10 Rope A2 A3 10 Barn A₂ A calf is tethered to one corner of a barn with a rope 90 feet long. The dimension of the barn is 10 feet by 10 feet. The calf can graze from A₁, A₂, and A3, as shown in the figure below. What is the maximum grazing area for the cow? [Hint: Read about Circle Sector to get area A₂]

Q: f(x, y) = 6√√√x – y²e- - a) b) y²e-3ry + | co y Find f and fy. Evaluate fazy (4,-1).

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Q: Find the horizontal asymptote(s), if any, of the curve f(x) = (x-x+) -16 Select one: Ⓒ x = 4, x=-4 O…

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Q: Let z = √√√7xy +9y, and x = s³ and y = 1². Use Chain Rule to find dz when t = 1 and s = 2. ds

A: To find out the given partial derivative.

Q: ) Consider a horizontal parabola of the form ay² +by+ c = x wherea #0 and whose graph contains the…

A: Given problem:- Consider a horizontal parabola of the form ay² +by+ c = x whose graph contains the…

Q: 1 Give the antiderivatives of X The antiderivatives of 1 2 are

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Q: 2 +81 1/s(3² +9) ²0 ds

A: The given integral is (s4+81)/[s(s2+9)].

Q: S sin² 2xcos² 2xdx

A: This question is based on indefinite integral using Trigonometric formula.

Q: (x³ − 2y²)dx + 2xydy = 0 -

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Q: z = (x + y)², x = s²t, y = st². Use the Chain rule to find dz for t = 1 and s = 2. ds

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Q: Question 1 [ Let 7 f(x, y) =ln(xy)-50x³y Find fx, fxy and fxyx.

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Q: Find the solution of the given initial value problem. y(4) 10y""+25y" = 0; y(1) = 10 +e5, y'(1) =…

A: This is a problem related to differential equation. Please follow the procedure given below.

Q: P₁: -60x + 90y + 120z = 29 P₂: 4x - 6y - 8z = 5 P3: -20x + 30y + 40z = 4 P4: 12x18y + 24z = 9

A: Follow the procedure given below.

Q: In(t³ + 1) + t³ + 1 r(t) = 4: then the limit lim r(t) equals 1-0 -i-(4e-²¹-5e²¹)j- - sin³t -k, 13

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Q: 2. y²dx + (x² − xy - y²)dy = 0 [Answer: (x - y)y² = c(x + y)]

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Q: Find the following using the table below. I 1 2 3 f(x) 1 3 4 f'(x) 4 1 g(x) 4 1 3 g'(x) 2 3 33 4…

A: Given that h(x) =fg(x). We have to find h'(3) that is derivative at x=3. Now, ddxh(x) =ddxfg(x)…

Q: Work Problem You must provide a clear and detailed solution for the question. Let 2 = (y - 2x) ³,…

A: To find out the partial derivative.

Q: The limit lim (x,y)→(-1,2) (x²y − 3xy²) = −8 - Select one: True False

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Q: z = (x + y)², x = s²t, y = st². Use the Chain rule to find d ds for t = 1 and s = 2.

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Q: 11. Determine whether the given quadratic function has a maximum value or a minimum value, and then…

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Q: x+3y=x².

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Q: 1. Find the domain of the vector function r(t) =

A: 1. Given Vector Function,rt = lnt+2, t1-t2, 2tt2 -4

Q: Let y=tan(4x+6)  Find the differential dy when x=1 and dx=0.1  Find the differential dy when x=1…

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Q: The limit lim (x,y)→(4,-5) exists and equals to Select one: O True O False 25x²-16y² -5x-4y -40

A: Given the limit is  limx, y→4,-5 25x2-16y2-5x-4y.

Q: Present a second order differential equation. Identify the corresponding auxiliary equation.…

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Q: Find the limit lim 3-0 Select one: 04/3 None of these Does not exist -8/6 00 8x² + 7x-9 6x²-2 if it…

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Q: Find all vertical and horizontal asymptotes of the graph of the function. (Enter your answers as a…

A: This question is based on vertical and horizontal asymptote.

Q: then the / r(t)dt is equal to r(t) = (-2 cos (21), 3 sin (4t), In (2t)), Select one: True where C is…

A: Please see the below picture for detailed solution.

Q: Is the scalar valued function f(x)=(x^2-1)/(x+1) continuous?

A: This is a problem related to limit and continuity of the function. Please follow the procedure given…

Q: x+2, The function f(x) = 2x², Select one: Ⓒ True False x≤1 1<x<3 is continuous from the right at x =…

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Q: The domain of the function f(x, y) = 3xy 2+√4x2+y2-16 is:

A: Given problem:- fx,y=3xy2+4x2+y2-16  To find:- Domain of f(x,y)

Q: Which of the following is the answer of x² - y² ·? lim (x,y) (5,5) 2x - 2y Select one: -5 O 5/2 05 O…

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Q: Use the First Fundamental Theorem of Calculus to find F"(x) if = [*_ sinh√/1 +ť² dt. F(x) =

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Q: Solve: x²y + 4xy' + 2y = 0 Indicial roots: r₁= General Solution: y = C₁ a.x-1 b. x3 c. xinx d. e3x…

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Q: Use Leibniz's rule to find 히증 11 Textbook dx for y= 0 S 7x² 8t - dt. 8t+1 Ask my instructor

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Q: z = √xy, dz dt t², y = -t² then 2 2 2t²) =?

A: We have to choose the correct option from the given options according to the given information

Q: 4. (xy² + 2x²y³) dx + (x²y - x³y²) dy = 0

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Q: If z = √√√xy, dz and x = t², y = 1² then =? dt Select one: O √xy(21) O √xy(21²) 0 2t O None of them…

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Q: Let z = √7xy +9y, and x = s³ and y = 1². Use Chain Rule to find dz when t = 1 and s = 2.

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Q: Question then the range of f is the interval [0, 12]. Select one: O True : If f(x, y) = 3√/16 - x² -…

A: This question can be solved using the concept of domain and range of multivariable function.

Q: E A4 sin (e-² + ln z) + C 4 sin (-e-²) + C B O A § 4 (½ − e¯²) cos (e¯² + Inz) dz B E None of the…

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Q: (5x¹2xy)dx + (6y+kx²)dy = 0

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Q: Work Problem 1( Let z=(y-x)³, and as(1 t) and y = st². Use the chain rule to compute da and da da

A: Given problem:- Here  z=(y-x)3  And x=s(1-t), y=st2  find using chain rule zs and zt

Q: 4. Graph the equation: f(x): = 1, -2x + 4, -2, -3≤x≤0 0 ≤ x ≤ 3. x > 3 -1 5+ 44 3- 2+ +1 -1- -24 -3-…

A: This is a graph of piece wise function

Q: 2. Evaluate x² dx (x-1)(x² + 4x + 5)

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Q: Determine whether the lines L₁ and L₂ are parallel, skew or intersecting L₁: x = 4 + 2t, y = -5 +…

A: L1 : x=a1+b1t , y =c1+d1t , z=e1+f1tL2 : x=a2+b2s, y =c2+d2s , z=e2+f2sthen Lines L1 and L2 are…

Q: A rental company charges $65 a day and 20 cents a mile for renting a truck. Michael rents a truck…

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Q: If we use the trigonometric substitution sec(x) 5 then we get t = √25t² - 1=tan(x) Select one: O…

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Q: For the curve f(x) = Find the horizontal and vertical asymptotes. x-4x² +2 x² - 4x +4

A: This question can be solved using the concept of horizontal and vertical asymptote of rational…

Q: A rotating light is located 20 feet from a wall. The light completes one rotation every 3 seconds.…

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Q: lim x-x6-x O +∞ 00 ∞- O O 3 1 2 ||

A: topic - limits