For each of the following functions, find the domain (the allowed x and y values). Зху Z (х, у) %3D а. х-10 Z (x, y) = 3y? b Z (x, y) = In Z (x, y) = C. d. V2-x2

Q: Construct the inverse matrix (if it exists) for the following matrices: [12 61 (а) А %— 4 2. 1 -2]…

A: We will find out the required solution.

Q: 087(1.) 22 CITI T21 CT = т 210 3.23 х 10-23 та %3D (2.1× 10-10 ст)3

A: i have solved first question of second image for other question repost.

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

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Q: 4=6xt -11 t.

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Q: , (х, у) (0,0) x+y f(x.y)%3D (х, у) (0,0)

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Q: The natural domain of the two-variable function f(x,y)=(2x+2y^2)√ 2−x^2−y^2 is Choose an option:…

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Q: The range of y = v16 – x² is А. [4, со) В. (4, оо) C. [-4,4] D. [0,4] Е. (0,4)

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Q: 1- 3t - 2 t+1 - dt

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Q: If f(x.y)= x?+2xy+5y² then дудх

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Q: Find y, of the following functions: (i) y=e³x+2

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Q: Find &, for f(a, y) = xy? – 4.ry² +x*. 3

A: This question is related to partial derivatives.

Q: Find fxy when f(x, y) = 8xeXy.

A: To find fxy when fx, y=8xexy.

Q: Iff(x, у)%3ху + ух, then ( fy = xyx - 1 + xv.ln ( x ).

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Q: If g(x, y) %3D Vху — Зх, find gx and gy. gx %3D gy %3D

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Q: then If f(x,y)= x²y+ y, 3x O b. бху 6x O d. o

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Q: The relationship between y and z is given by the formula: z=y4-1.Are both quantities functions of…

A: z=y^4 -1 . For one value of y, there is only one value of z. So z is a function of y.

Q: Suppose that y varies directly as x' and inversely as w. If both x and w are doubled, what is the…

A: Given: y varies directly as x5 and inversely proportional as w2

Q: Find f, (x.y) if f(x.y)=x - 5xy- 4y2.

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Q: Differentiate y = (2х + 1) а. 2 y = (2х + 1) b. 1 y = 2/(2х + 1) 1 y = (2х + 1) d. y = (2х + 1) е.…

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Q: If the value of bo is negative, then the relationship: will not cause any impact to y values…

A: Regression line Y=b1x+bo  Where bo=intercept b1=slope

Q: 10. The y" of y = (2x¹ + 4x³)(3x¹ − x³) is - a. 336x6 +420x5-120x¹ C. b. 336x5 +420x4-120x d. 48x7…

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Q: For the function z = - 8x³ - 2y² - 2xy, find a z(1,-2), andz(1,-2). dz dz a ax' dy ax

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Q: If z varies direct to the square of y and y varies inverse to x (x,y,x) = (20,120,100) Then find the…

A: z varies directly to the square of y, so z=my2 y varies inversely to x, so, y=nx Therefore,…

Q: Differentiate first, and then substitute values for the variables. If the substitutions were…

A: Definition used -        Derivative of function at a point -         If we have to find the…

Q: If f.(x, y) = 13x + 8y + 11, || f.(3, 2) = a. b. f„(5, 2)

A: Given, fx(x,y) = 13x + 8y + 11 a). fx(3,2) = 13*3 + 8*2 + 11 = 39+16+11 => fx(3,2) = 66

Q: 1. (A×(DxB))x(Ex(A×C)) 2. BxC-(A×B )× D 3. Ric + Rn – Rp. EB 4. E.Ax(D×C)-B 5. D-(4-E)xE +(ВxЕ)xС+4…

A: As per our guidelines, we are allowed to answer only three subparts of a question. Since you have…

Q: y = Arccot x 2 Arccot /x Vx(1+x) А. Arccot x С. x* +x Arccot x Vx(1-x) Arccot x Vx(1+x) В. D. -

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.