2x² sin x + 3y³ lim (x,y) →(0,0) 3x³ + 2y² if we approach along y-axis, we will get 0. Select one: O True O False >

Q: The following limit lim Select one: None of them O does not exist. equals 0. equals 1/3 O equals 1…

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Q: A dam has a semi-circular gate at the bottom that is 4 m in diameter. The dam is 12 m high and…

A: Given data as follows :- Diameter of the semicircular gate is 4m. Height of the dam is 12 m.  Water…

Q: find the rate of change of the circumference of a circle when the area is increasing at the rate of…

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Q: Work problem 2 (1 Let w(x, y) = 5x - 5y - x² + 5y³, x = cos(t) and y = -sin(3s). Use chain rule to…

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Q: Work Problem for the question. Let where x = t = -1. You must provide a clear and detailed solution…

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Q: In³ w 3 w√In²w-4 mp

A: Given :∫ln3wwln2w-4dw

Q: Evaluate: cot¹ (+) -do None of the choices Ocot³ (1)-cot ()- tan³ () - tan() - ○ cot³ (1)- - tan() -…

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Q: If f(x, y) = A In (x² - y) -x+y+1 O {(x, y) x² > y, {(x,y)|x² ≥ y, ○ ○ {(x, y) x² > y, | then the…

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Q: Question 1 f(x, y) = 4xy 2x²+5y² Consider the function a)!* s Find the domain of f. b) [₁ Show that…

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Q: Evaluate: 0 tan¯¹ (0) do

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Q: What is the area (in square

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Q: a) b) exist f(x, y) = x²yesy 8x²+7y² Find the domain of the function f. Show that lim f(x, y) does…

A: According to question,Given Function,fx, y = x2 y e5y8x4 + 7y2

Q: Given the functions f(x, y) = 4 cos(4x - 6y) and g(x, y) = -6 cos(4x - 6y). af The partial…

A: Here we have to use the concept of partial derivatives

Q: Question 40 The graph of y=2 is concave downward for all values of such that. 0 x 2 0x 0 < Previous

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Q: A road perpendicular to a highway leads to a farmhouse located a = 1.5 km away. An automobile…

A: This question is based on application of derivative.

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: Question a) b) C g(x, y) = (0,0). x³-4xy Let f(x, y) = x²-2y Find the first partial derivatives of…

A: Let fx, y=x5-4xy2x2-2ya To find the first partial derivatives of f.b To determine whether the limit…

Q: if u=f(x,y), x=g(w) and y=h(w), using chain rule, what is ∂u/∂w?

A: Silution : Given that u = f(x,y)

Q: Solve the initial value problem: dy dz 9y, y(0) = 1

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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: The domain of f(r. y) = Select one True False 19-y V is the upper half of the disc centered at…

A: fx,y=9-x2-y2y

Q: f(x, y) = 6√x - y²e-³xy е a) b) + elw Find få and fy. Evaluate frzy (4, −1).

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Q: The solution of the following non exact differential equation (cos x) dx + (1+² sin x)dy = 0 is:…

A: The given differential equation is;  Cosx dx +(1+2/y Sinx) dy=0

Q: 8x³ - y³ 3 lim (z,y) (1,2) 2x - y Select one: O equals 12. O equals 0. O None of them O equals 4. O…

A: Lim(x, y) -(1,2)(8x3-y3)/(2x-y).

Q: The domain of the function f(x, y) = Inz x-y is: Select one: O The region below the line y = x but…

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Q: If you can only answer one, please answer 99. The questions asks whether the series converges or…

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Q: Use the Divergence Test to determine whether the following series diverges or state that the test is…

A: This question can be solved using the concept of divergence test.

Q: If f(x, y) = 2√/16 - x² - y², then the domain of f is the set D = {(x,y)|x² + y² ≤ 16}. Select one:…

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Q: Question Select one: equals 4. None of them does not exist. equals 12. equals 0. 8x³ - y³…

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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: What is the angle of inclination? x +₂y + 8 = 8=0

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Q: A solid figure projects the same shape on the x-y, y-z, and x-z view. Which of the following…

A: A solid object have same shape on x-y, y-z and x-z view.

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

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Q: Find the directional derivative of the function at P in the direction of v. f(x, y) = x³y³, P(8, 3),…

A: Here we have to find the direction derivative.

Q: Question 38 The critical point of f (x) = (sin x) (cosa) on the interval (0, π/2) is at x = Ono…

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Q: Estimate the area under the graph of f(x)=1/x+1 over the interval [3,7] using ten approximating…

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Q: Use the gradient to find the directional derivative of the function at P in the direction of v. h(x,…

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Q: Jolene invests her savings in two bank accounts, one paying 3 percent and the other paying 10…

A: topic- simple interest and equations

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: The function f gives the weekly profit, in thousand dollars, that an airline makes on its flights…

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Q: Find the point of inflection of the graph of the function. (If an answer does not exist, enter DNE.)…

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Q: A square is increasing in area at a rate of 20 mm² each second. Calculate the rate of change of each…

A: topic- application of derivatives

Q: graph 10 5 0 answer 5

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Q: A road perpendicular to a highway leads to a farmhouse located a = 1.5 km away. An automobile…

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Q: If f(x, y) = 9x² - 6y³ - 7 cos(-6xy + 플) then Select one: O True O False fy(л,0) = -42

A: Given function is f(x,y)=9x2-6y3-7cos-6xy+π2. We have to find fy(π,0) that is partial derivative of…

Q: Which of the following sets of vectors in R³ are linearly dependent? Note. Mark all your choices.…

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Q: given z=xlny-((2^x)/y)+ysinhsqrtx, find (∂^4)z/∂x∂y∂x∂y

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Q: ax+ 2 x ≤ 2 f(x)=4-x², 2<x<3 2x+b. 3 < x Find the value of a so that f(x) is continuous at 2. Find…

A: To find out the value of a as f(x) is continuous at 2.

Q: Evaluate: 0 tan-¹ (0) de Ô arctan(9)–0 2 arctang+ -arctan0+C 0—arctan(0) +C

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

A: We can solve this as follows: