Letf(z) 3z-2i. Find the maximum valne of /(=} on the disk z<.

Q: #2. Consider the function f (x,y) = x +y-xy on the set D which is the closed triangular region with…

A:

Q: Find the maximum and minimum values of ƒ(x, y, z) = x - 2y + 5z on the sphere x2 + y2 + z2 = 30.

A:

Q: Find the maximum value that ƒ(x, y, z) = x2 + 2y - z2 can have on the line of intersection of the…

A: Given and planes are

Q: ® Find the_functian that satisfies the following conditions for some constant Eceficients c,and c…

A:

Q: the surface z = &x + 4y th=

A:

Q: 1. Find the absolute maximum and minimum values of the function 2u2) on the set D where D is the…

A: We have been given the function f(x,y)=e-x2-y2(x2+2y2)      (1) on a set D x2+y2≤4 where D is the…

Q: Use the method of Lagrange multipliers to find the maximum of the func- tion f(x, y) = x² + xy+y² on…

A: Find the maximum of the function fx,y=x2+xy+y2 on the unit circle x2+y2=1 using the method of…

Q: 4) Consider the images of the hyperbolas x² – y² = ±c² under the mapping f(z) = z², where c > 0.…

A: Given the hyperbolas x2-y2=±c2, c&gt;0. We need to consider the images of these curves under the…

Q: fj+1 - fj-1 2Ax Assuming a uniform grid spacing of Ax, derive a finite difference approximation to…

A:

Q: 8. (a) Show that the system i=y+xf(r)/r, j=-x+yf(r)/r (7=x²+y?) (*) has limit cycles corresponding…

A: Given part (a) x·=y+xfrry·=−x+yfrrr2=x2+y2 By transforming coordinates into polar coordinates Thus…

Q: Integrate G(x, y, z) = xyz over the triangular surface with vertices (1,0, 0), (0, 2, 0), and (0, 1,…

A: To Determine: integrate Gx,y,z=xyz over the triangular surface with vertices (1,0,0),(0,2,0) and…

Q: find the absolute minimum and maximum of f(x,y)=2x^3+y^4  over the disk x2+y2 ≤ 1

A:

Q: Use Lagrange's multiplier(s) to find the maximum and minimum for f(x, y, z) = x² + 2x + 2y2 + 3z2 on…

A:

Q: Find the maximum value of f(x, y) = 9xy(5 – 25x – 5y) over the triangle with vertices (0,0), (, 0)…

A:

Q: Find the ab solute moximurn ond minimum volueso the function triongulor region with vertices…

A: Differentiate the function fx,y=x2+y2-x-y+1 with respect to x and y, to obtain fx, fy, fxx, fyy and…

Q: 3. Find the area of the part of the surface x 2z + y° - 3, that lies above the triangle in the…

A: Given, x=2z+y2-3, i.e. z=12x-y2+3. As it is known that the surface area is given as,…

Q: Find the maximum and minimum outputs for the function f (x,y) = xy – y² on the portion of the disk…

A: The given function is f(x,y)=xy-y2    ....(1) Let g(x,y)=x2+y2-1=0    ....(2) h(x,y)=x+y-1=0…

Q: Find the maximum volume of a box that is resting on the xy-plane with one vertex at the origin and…

A: Given the plane is 3x+4y+2z=12

Q: * Use the Grom Schmidt process for thi two_ dmensional space: 2 3. 4 2

A: Gram Schmidt process is given by: uk→=vk→−∑j=1k−1uj→⋅vk→|uj→|uj→   v1→=201, v2→=3-51, v3→=042,…

Q: Find a parameterization for the quarter sphere x² + y² + z² = a² where z > 0 and x > 0.

A:

Q: & 10 Let 20xx,y)=x² be a function defined by on al disk I in the positive quadrant containing the…

A:

Q: Find the orthogonal trajectories of the family of curves: Ellipses with centers at (0,0) and two…

A: Given ellipse with centers at (0,0) and two vertices (1,0) and (-1,0).

Q: 6. Determine the number of zero's for h(z) = 2z* – 3z² + 2z – 5 inside the disk |z| = 2. (Use…

A:

Q: let f (z) = z2 + z find the maximum value of If(z)l A = {z € C:0 < x, y < 2} on the square

A:

Q: 6. Determine the number of zero's for h(z) = z-2z + 9z2 + z-1 inside the disk |z| = 2. (Use Rouche's…

A:

Q: Let P be the plane 2x + y – z = 2 and let Q(1,0,3) be a point. We want to find the minimum distance…

A:

Q: If the function f is defined on the disk x2 + y² < 1, then f has a critical point somewhere on this…

A:

Q: Find the maximum and minimum values of a function F(x,y.z)3D8X+y+ z on the surface A

A:

Q: d the integration norm of the giver x) = -9x + 2

A: In this question we will use basic of calculus i.e integration. We will simply integrate the given…

Q: Find the residues of f(z) = z²-2z (z+1)²(z²+4) at all its poles in the finite plane.

A:

Q: Let A ∈ M nxn(F). Show that A is diagonalizable if and only if At isdiagonalizable

A:

Q: Find the maximum modulus of the function f(z) = -iz + i, |z| < 5.

A: Find the maximum modulus of the functionfz=-iz+iz≤5

Q: z? f(2) = 1-z* 4

A: We use the fact that the 1/(1-z)= 1+z+z2+z3+z4+......

Q: Show that the only possible maxima and minima of z on the surface z = x3 + y3 - 9xy + 27 occur at…

A:

Q: Let C be the boundary curve counterclockwise of the semidisk x2 + y? < 9,y 2 0. Then f (-2ydx +…

A: Given Information -  C is the boundary curve counterclockwise of the semi disk x2 + y2 ≤ 9 , y ≥ 0…

Q: 4. Find all local extremum of the functionf (x,y) = x2 – y2 bounded by the circle x2 + y2 = 1: %3D

A:

Q: Find the maximum value of  f(x,y,z)=27x+7y+3z on the sphere x2+y2+z2=81

A: For this question we will use Lagrange multipliers where f(x,y,z)=given function and…

Q: Let f(x,y) = 4+xy – 2x – y and let T be the closed triangular region with %3D vertices (1,0), (5,0),…

A: We have to determine the absolute maximum and minimum values of f on T.

Q: Find the maximum value of f(x,y,z)=9x+15y+9z on the sphere x2+y2+z²=100

A:

Q: 5) Let R(x, y) = 3x² + y². Find the minimum value of R on the hyperbola xy 2.

A:

Q: Find the absolute maximum and absolute minimum of f(x, y) = yx² – y² +4 on the unit disk {(x, y) :…

A:

Q: The minimum value of f(x,y,z) = x^2 -2y + 2z^2 on the sphere x^2 + y^2 + z^2 =1 is ....?

A:

Q: (a) Find max, min or saddle points for the surface Z= x* - 3xy + 5x

A: We have to find first and second order partial derivatives.

Q: Find the Jacobian of following functions f(x,y, z) = 3xy – yz + 2y z2 - 5xyz3 g(x,y, z) = xyz -…

A:

Q: Let C be the boundary curve counterclockwise of the semidisk x² + y? 0. Then § (-2ydx + 3xdy) = a)…

A:

Q: Let C be the boundary curve counterclockwise of the semidisk x² + y? < 9,y 2 0. Then f(-2ydx + 3xdy)…

A:

Q: let f(z) = z2 + z find the maximum value of If(z)| on the square A = {z € C:0 < x,y < 2}

A: We have given function fz=z2+z where, z=x+iy complex number We have to find maximum value of fz on…

Q: Verify Green's Theorem in the plane for F = (x² + y²)î + (x² – y²)f in the anti-clockwise direction…

A:

Q: *6. Let f: R' →R be given by =+4x'z-6xyz+4y-3x'y. Is M=f-((0}) a smooth surface (2-dimensional…

A: Given, fxyz=z2+4x3z-6xyz+4y3-3x2y2 Now, writing the given function in matrix form.…

Q: 2) Find the area of the part of the surface z = x2 + 2y that lies above the triangle with vertices…

A:

Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.