af and Әх ду af af Find az 2 f(x, у, 2) x2 + y2 + z2 af ax af ay af az Find their values at (0, -1, 1) if possible. (If an answer is undefined, enter UNDEFINED.) af (0,-1, 1) = ax af -(0,-1, 1) = ду af (0,-1, 1) az 00 IL II

Q: (x+1)+-y² Suppose g(x, y) = {(x+1)++y² ' (-1, if (x, y) + (0,1) if (x, y) = (0,1) Find g,(0,1) and…

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Q: Partial derivatives Let f(x, y) = x³ – y² + 4. af a. Compute af an b. Evaluate each derivative at…

A: First we differentiate with respect to x Then we differentiate with respect to y

Q: 2-y'-1 x-1 3 If f(x, y) = ,x + 1 ,x = 1 then f, (1,0) – 2f:(1,0) = x3 -y3 -1 If f(x, y) , X 7 1 x-1…

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Q: If f.(a,b) = f,(a, b) = 0 then (a, b) is %3D %3D ans. critical point point of extreme isolated point…

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Q: F(x) = x^4/5(x-8)^2 Find the critical numbers of the function Find the values of x in the domain F…

A: F(x) = x^4/5(x-8)^2 Find the critical numbers of the function Find the values of x in the domain F…

Q: Assignment O Show that H(X/Y)=H(X,Y)-H(Y) H(Y/X)=H(X,Y)-H(X) And 1(x; Ү) — Н(х) — Н(х\Ү) %3D Н(Ү) —…

A: Solution for first part: We have to show H(X/Y)=H(X,Y)-H(Y)                      (*) Since H(X/Y) is…

Q: Function 1: x= y 2/3 Function 2: x = y Rotation: x - axis Interval: [0, 3] 3+ 3, 3) 2.5+ 2+ 1.5+ 1+…

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Q: Find values of x and y such that  fx(x, y) = 0 and fy(x, y) = 0  simultaneously. f(x, y) = ln(x8 +…

A: Answer

Q: Rule: Rule: a. IN (x) b. OUT (y) 8. IN (x) OUT (y) IN (x) OUT (y) с. 3 -9 0.5 0. -2 10 37 -4 -10 -1…

A: As per bartleby guidelines we only give first three question answers.

Q: Chain Rule with one independent variable Use Theorem 15.7 to find the following derivatives. dz/dt,…

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Q: function √x² + y² + 1 x² + y² 2 f(x, y) = 1 if (x, y) = (0,0) 2 2 (x, y) = (0,0). If not, classify…

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Q: 4 0 -2 2 0 4 2 6 Which statement about the functions is true? A. The initial value in function T is…

A: We have to check

Q: Function g(x,y) is differentiable everywhere. Classify its critical point (0,-2) if the following is…

A: Given that g(0.-2)=-2gxx(0,-2)=-1gyx(0,-2)=2gyy(0,-2)=-5

Q: QI: Put True or False and in front of the statements and give the reason. 1. If the point Pis a…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: x-y-1 If f(x, y) = ,x + 1 x-1 3 , x = 1 then f,(1, 0) + 3 fx(1,0) =

A: We have to solve

Q: af and дх ду af af Find az f(x, y, z) = 5xy + 5xz - 5yz af дх af ду af az Find their values at (0,…

A:

Q: Verify the natural domains and associated ranges of some simple functions.The domains in each case…

A: Hey, since there are multiple sub-parts posted, we will answer first three sub-parts. If you want…

Q: lim f(x, y) = 6, then f(1.9, 2.9) = 6- %3D (x, y) + (2, 3) If f(4, 5) = 3 Vf(4, 5) = (-3, 2) then…

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Q: Verify the natural domains and associated ranges of some simple functions. The domains in each case…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: function is in a form of y = ax^3 + bx^2 + cx + d. It has relative maximum at (3, 3) and point of…

A: Here we use the basic concept of differentiation for finding the relative maximum and point of…

Q: 8. If f(x, y) = 2x? xy, find f (2,3) and fy (2,3). - 9. If f (x, y) = find f; (1,0) and fy(1,0). 10.…

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Q: The productivity of a country is given by f(x,y) = 13.34x yr, where x is the amount of labor and y…

A: The productivity of a country is given by fx,y=13.34x0.422y0.578, where x is the amount of labor and…

Q: Could I get help finding the fx(X,Y) and fy(x,y) with the attached problem please

A: The given function is

Q: əz and ду az of the function xsin(y+ z) – xy + z² = 2y. Find the ax

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Q: Calculus O 201 6 Kuta Softw are LLC. A11 Name rig hts reserved. ID: 1 Motion Review Date Period A…

A: Note : There are many subparts and questions in the given questions. So I will answer the first two…

Q: Cauchy-Riemann equations. Show that for a family u(x, y) = c = const the orthogonal trajectories…

A: Here we need to prove that the two family of given surfaces u(x, y) = c and v(x, y) = c* are…

Q: If x'-y-1 f(x, y) = ,x 1 %3D X-1 3 ,x = 1 then fy(1, 0) + 3 fx(1, 0) = %3D -6 does not exist O 6 0…

A: Lets find.

Q: The linearization of the function f (x, y, z) = x³z² + xy2 + 3y - 10 at the point (-1, 1, 2) is…

A: L(x,y,z)=f(a,b,c)+fx(a,b,c)(x-a) +fy(a,b,c) (y-b) +fz(a,b,c)(z-c).

Q: 3. Consider the function f(x) = x3 + 3x2 – 45x + 5, then %3D I. fis decreasing on (-5, 3) and…

A: Given   f(x)=x3+3x2-45x+5  f'(x) = 3x2+6x-45For critical points f'(x) =…

Q: Problem. Let f(z, y) be a function such that f(2, 3) = 0.8, f.(2, 3) = 3.9, f,(2, 3) = 0.4. Jse the…

A: Here, given that  f(2,3)=0.8, fx(2,3)=3.9, fy(2,3)=0.4 Now, to approximate f(2.01,2.99) using the…

Q: V2= 15, a = 0.05, and F critical value = 2.33. Find V1: Answer:

A: V2= 15, a = 0.05, and F critical value = 2.33. Find V1: Answer:

Q: Determine if the function satisfy the Cauchy-Riemann equations. f(z) = z²

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Q: Let the line PQ pass through the points P = (-4,-4, -6) and Q = (-2, 1, - 16). The line will pass…

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Q: Let f(x, y) = x + 2xy-2x-4y be a function in x and y, then: a. (2,3) is a critical point b. (-2,-5)…

A: The critical point is a point where fxa,b=0 and fya,b=0 or fxa,b=0 and/or fya,b=0 does not exist.

Q: ((x+1)ª-y² Consider the function g(x, y) = {(x+1)4+y²' -1, if (x, y) # (-1,0) if (x, y) = (-1,0)…

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Q: Cramer's Rule iF poccible : 3x + 2y + 2 z a. y + 2z = -1 2x + 2y +

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Q: 3. f(x) = --x- 1) + 2 4. f(x) : :--x+1- 5 Starting Pt: Inc or Dec: Starting Pt: Inc or Dec: Domain:…

A: Solution is here

Q: 9. and 4.3-10. Let f(x) hylx)%3D1/(10-1), y x ) = 1/10, * = 0, 1,2.. , x+1.... r+19.Find (a) f(x,…

A: The given information: fx=110, x=0, 1, 2, .......9hy|x=110-x, y=x, x+1, x+2.....9

Q: 6- 4- 2- f10 -8 -6 -2 2. -2- 4+ -6- (a) The function f is decreasing over which intervals? Choose…

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Q: Function 2 Function 1 ((-4,-5), (0, - 4). (4, - 1). (8, 3) {(-5, 5). (-4, 3), (–3, 1), (-2, 3)} O…

A: We know that a function is linear if the x values and y values have constant rate of change.

Q: Sк) — (-5,2), (J2.3), (3,0), (л,-), (14, ) s(x)- {-1,я), (2, /2), (3,-1), (4,3)} Кx) — 2x* -18 k(х)…

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Q: Are the functions f, g, and h given below linearly independent? f(x) = et – cos(5æ), g(x) = e* +…

A: The functions are linearly dependent :

Q: 12) f(x, y) =x'+y'+3x-3y² -8 Ans. f(0,0) saddle point, f(0,2) =-21 local min., S(-2,0)=-4 local…

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Q: V f(x = - (x – 8) (x – 15) V g(x) = -x + (10,15) 15 V Label: (10, 15), (14,9) V Label: 10 (14, 9).…

A: To find the area of region enclosed by functions f and g

Q: Statement 1 : x(y-z) =xy+xz Statement 2: xyz + xyz + xyz = xz + xyz Statement 1 : True Statement 2:…

A: In Boolean algebra, the minus sign or bar sign are used to mean not or negation . As in statement…

Q: 2. Function g(x,y) is differentiable everywhere. Classify its critical point (0, -2) if the…

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Q: PLS HAVE A NEAT PENMANSHIP

A: We have to solve

Q: x, y > 0, x + y < 1 Determine the global extreme values of the function f(x, y) = 2x + 2x²y + y, f…

A: Given : f(x, y) = 2x³ + 2x²y + y² , x,y ≥ 0 And g(x, y) = x + y ≤ 1

Q: A real number, there is a relationship between the two functions let v(x,y) = xsin(t") - ycos(t") ,…

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Q: Q/Equation of line pass through the point (1,1,1) and parallel to z-axis is: Ans 1/ x=t , y=t+1 ,z=t…

A: Point direction form of the equation of a straight line is- (x - x1) / a  =  (y - y1) / b = (z - z1)…

Compound Probability

Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent. 

Tree diagram

Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described. 

Conditional Probability

By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.