Consider the function. f(x, y) = 9 7 9 Find Vf(x, y). Vf(x, y) =

Q: How many independent variables does the function r(t) = ⟨ƒ(t), g(t), h(t)⟩ have?

A: Given that the functions f, g, and h, all depend on t. t is independent So there is only one…

Q: Consider the function. f(x, y) = 7 -- 9. 5 Find Vf(x, y). Vf(x, y) =

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Q: Approximate f(3, 5) using the contour diagram of f(x, y) shown below. 18 12 10 6 X=2 10

A: Consider the given contour.

Q: A r&r.'Find y as a function of t if 9y" – 24y' + 7y = 0, and y(5) = 3, y' (5) = 8.

A:

Q: 3. Find V x F for F(x, y, z) = -IZ i+ x² + y² -yz 1² + y² +√x² + y²k.

A:

Q: 4. For what values of the constant a is the following function concave/convex? f(x, y)= -6x2 +…

A: Will be using definition of concave/convex for function of two variables

Q: Q/ Let X be the r.v such that E (X) = 2 , E(X²) = 2a , E((2+aX)²) = 2a³ Find the value of a

A: We have given that, Let X be the r.v such that E (X) = 2, E(X²)= 2a , E((2+ aX)²) = 2a3 We want to…

Q: Find a function r(t) for the line passing through the points P(0,0,0) and Q(4,2,1). Express your…

A:

Q: Find V (V x F), if F(x, y, z) = 6ei+ 9xe'j - 5e k. V. (V x F) = %3D

A: Given Fx,y,z=6exzi+9xeyj-5eyzk

Q: 7 For the function f(x,y) =x' e Oxy, find fy, fy, f,(- 1,5), and f,(1,3). x' 'y'

A: take the partial derivative with respect to x

Q: Q (1): Find fxyz for the function: = xe² + ye* + zey a) f(x, y, z) %3D

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Q: f(x, y) = (-x – 2y, x – 4y).

A: Follow the steps.

Q: Evaluate V7 by using linear approximation of f(x) = V about the value I = 8.

A:

Q: 16. Find the values of r so that the function y= e™ satisfies the equation y" – 4y' – 21y = 0. A)…

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Q: Consider the function. f(x, у) %3D 14 — 10 3 Find Vf(x, y). Vf(x, y) =

A: as per our guidelines, I can answer maximum only one question. Since you have asked for multiple…

Q: 2. Find whether the function F = (x -y')i+ – 3x)7+(z² - xy )k i %3D

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Q: The function z = f(x, y) = 2x + xy – y? %3D %3D - is given, where x = g(y) = 3y? %3D

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Q: Find f(x, y) and fy(x, y). 25. f(x, y) = y3/2

A: The given function f(x,y)=y-32tan-1xy

Q: Find all points (x, y) where the functions f(r), g(x), h(x) have the same value: 8 S(z) = 2"-5 + 3,…

A: Given function are: fx=2x-5+3gx=2x-5hx=8x+10 Equating function g(x) and h(x),…

Q: Q/ Let X be the r.v such that E (X) = 2, E(X²)= 2a , E((2+ aX)²)= 2a3 Find the value of a .

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Q: Consider the function. f(x, y) = 11 5 7 Find Vf(x, y). Vf(x, y) =

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Q: Consider the function. f(x, y) = 20 10 4 Find Vf(x, y). Vf(x, y) =

A: Th given function is:fx, y=20-x10-y4To find ∇fx, y

Q: Q3: Let f(y) = Ly]. Find a) f'({0}). b) f'({-1, 0, 1}). c) f'({y | 0 <y< 1}).

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Q: The function f has the property that f(3)=2andf (3) = 4. Using a linear approximation to ff near x=3…

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Q: Determine the expression for Fyz(x, y, z) given the function F(x, y, z) = 2x²y – xz? 3y z.

A:

Q: b. Find and sketch the domain of f(x, y, z) = Vz-x² – y²

A: (b) domain of function f(x,y,z) is set of those values of x,y,z where function f(x,y,z) is defined…

Q: The function, r= 3t°, y =ť –t is concave upward on the interval (a) (-∞,0) (b) (0, 0) (c) (-0,0) (d)…

A: The general form of the parametric equation of the curve in two-dimensional space is given by…

Q: b) If it is possible, find the function f(x, y) = u(x, y) + iv(x, y). where u(x, y) = x2 + 2xy- y²…

A: That's easy. Have a great day!!!

Q: х%3D1, 2, 3, Let f(x)= - otherwise a. Find G,(t). b. Use G,(t) to find V(X).

A: The probability mass function of X is, (a) The value of is,               Therefore,

Q: Find the domain of the function. f (x) = VI– 2z BIUA · A - I Z 3 田 GO

A: Domain is the value of variable x for which the function f(x) defines.

Q: Find a function r(t) for the line passing through the points P(0,0,0) and Q(5,7,1). Express your…

A: Solution:

Q: Using linear approximation of f(x,y)=*+Y at (3,2), the value of f(2.94,1.94) estimated to be x-y

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Q: Find Vf at the given point. 3 f(x,y,z) = x³ + y² − 4z² + z lnx, (1,5,3) Vf|(1,5,3)+(+()k (Simplify…

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Q: (s) Find and sketch the domain of the function. (a) f(x, y) = Va2 + y², z < 4 (b) f(x, y) = V1– x² –…

A: Given that f(x,y)=x2+y2 , z≤4x2+y2 ≤4Domain (x,y) ∈R2x2+y2 ≤16The closed disc centered at (0,0) with…

Q: Consider the function. y f(x, y) = 20 6 4 Find Vf(x, y). Vf(x, y) =

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Q: f(x, y) %3D 3ху + у? (а) f(x + Дх, у) f(x, у + Ду) — f(x, у) - (b) Ду Зх + 2y + Ду Ду # 0

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Q: Consider the function f(x, y) = x² – 6x + y? –- 2y + 10. Sketch the domain of the function h defined…

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Q: find the specific function values. ƒ(x, y, z) =(x - y)/(y2 + z2) ƒ(3, -1, 2)

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Q: +S,f= V2 2R then the constants R TCX If f(x) Rsin .2 and f(x)dx %3D and S are respectively.

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Q: Use linearization to estimate v26. Use L(x) = f(a) + f'(a)(x – a), where f(x) = vx and a = 25. Once…

A: Linearization formula L(x)=f(a)+f'(a)(x-a)

Q: ôf What is for the same function f = x*y+3y'z² ? ду X,Z

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Q: Which functions are linear? 1 Select all that apply. 3D%= A z = 5y + 10 82 = 7y- 10 =D= C2= 5y³ + 4…

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Q: Find Vf at the given point. f(x,y,z) =x2 +y2-4z2 + z Inx, (1,1,3) Vfl(1.1.3) + +k (Simplify your…

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Q: 5. approximate the number V0.9. Find the linear approximation of the function f(x) = v1 – x at a = 0…

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Q: Find the linearization L(x,y) of the function at each point. f(x,y) = x? + y? +1 а. (4,1) b. (3,3)

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Q: Find the linearization L(x,y) of the function at each point. f(x,y) = x2 + y? + 1 а. (3,4) b. (0,2)

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Q: Q/ Let X be the r.v such that E (X) = 2, E(X²)= 2a , E((2+aX)²)= 2a³ Find the value of a.

A: E(X)=2E(X2)=2aE((2+aX)2)=2a3

Q: Find V (V x F), if F(x, y, z) = 6ei +9rej - 7ek. V. (V x F) =

A: To find ∇·∇×F, if Fx, y, z=6exz i+9xey j-7eyz k.

Q: xy Find the linear approximation to the equation f(x, y) = 2, at the point (2,6,4), and use it to 3…

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.