A: find the analytic function whose imaginary part is zero.

Q: Ax, y) = In(x +y)

A: In this question, we have to find the domain and range of f(x,y)=lnx+y As we know that the domain of…

Q: В. B. Show that the function f (z) = -i z2 is analytic.

A: The solution is given as

Q: Consider the function f(x) = xn , where n is odd. Does f −1 exist? Explain.

A:

Q: Verify the Rolle's Theorem for the function (x2-1)(x-2) on [-1,2] find the point in the interval…

A: Given function is : fx=x2-1x-2 To verify the Rolle's Theorem and find the point in the interval…

Q: ): Apply Rolle's theorem for the function f(x) = 9x² – 36x + 27 over the interval [1, 3]. Justify…

A: Given :- Apply Rolle's Theorem for the function fx = 9x2 -36x + 27 over the integral 1,3.

Q: The domain of the function ,y) = In[x* +y² – 1) is:?

A:

Q: Consider the function y = 5cos(x). What are the exact values of C in the interval [0, 2pi] such that…

A:

Q: Is there a real function f(x) that is differentiable only at a point x?

A:

Q: Express the area A of an isosceles right triangle as a function of the length x of one of the two…

A: We have to express the area A of an isosceles right triangle   We have to write area as a function…

Q: Find thei maginary part of an analytic function whose real part is e(xcosy – ysiny

A:

Q: Explain which the function are analytic or not: F(z) =2xy – i(x² –- y²) |

A: A function fz=fx,y=u+iv , where u and v are functions of x and y, is said to be analytic if it…

Q: Locate and classify the local extremum of the function f (x, y) x² + y? – 8x – 2y + 6. | -

A:

Q: f(r) = 2r² - e² %3D

A:

Q: 1+x? b. y = 2 1-х*

A: The solution are next step

Q: The function f(z) is analytic if

A: analytic functions are functions which are locally given by the convergent power series. i.e any…

Q: What is the domain of the function f(x, y) = x² /ỹ – In(x)?

A: topic -  function domain and range

Q: What does it mean for f to be differentiable at a ?

A: we have to define that what we mean by the f is differentiable at a.

Q: What is T3 centered at a = 3 for a function f such that f (3) = 9, f' (3) = 8, f'' (3) = 4, and f'''…

A:

Q: Determine the points at which the function is not analytic: (iz^3 + 2z) / (z^2 + 1)

A:

Q: (b) Find the domain of analyticity for g(z) = e¥e!*.

A: We need to find the domain of analyticity for Therefore, we have…

Q: We can not find an analytic function f=u+vi such that 3u-v is not harmonic. * True False

A:

Q: Explain why Rolle’s Theorem cannot be applied to the functionƒ(x) = | x | on the interval [-a, a]…

A: Given- fx=x To explain- why Role's theorem can not be applied in the above function. Concept Used-…

Q: Express the function in the form   f ° g  ° h

A: The given function is Rx=x-1 It is required to show the given function in the form of fogoh. So,…

Q: B) If the imaginary part of an analytic function is 2x(1 – y), determine its real part.

A: Given- The imaginary part of an analytic function is 2x1-y. To Find- The real part of the analytic…

Q: a) Investigate whether the function f(z) = z is analytical?

A: In order to investigate whether the function is analytical or not, first write the function f(z) in…

Q: Describe the x-values at which f is differentiable.

A: Definition used -                       A function f(x) is differentiable at any point -…

Q: Find the imaginary part of an analytic function whose real part is e* (xcosy - ysiny).

A: it will be satisfy CR law equations

Q: y= V> +In(5x) Differentiate the function

A: Given,           y=x2+ln5x

Q: 1. Decide if there is an analytic function f (x + iy) whose real part satisfies Re(f) = xe".|

A: Given problem: To decide analytic function fx+iy whose real part satisfies Ref=xey.

Q: State the interval of the function g(x) = E-x is %3D

A: The given function is gx=32-x  exist in the interval (-∞,32] and does not exist in any other…

Q: Find for the following function: 1- y = etan'x 2-x'y+ x*y 2 at x = 2

A:

Q: Find the global maximum and global minimum of the function f(x)=sinx−x in the interval [−π,π].

A:

Q: Determine if the function f (z) = y + xi is analytic. you must show detailed work

A: we have to check if the function  f(z)=y+xi

Q: Find an analytic function whose real part is e-x (xsiny+ycosy)

A:

Q: Find the domain of the function. Express the exact answer using interval notation. f(x) = To enter…

A: Consider the function  f(x)=25x+8

Q: Find the analytic function whose imaginary part is v =2xy

A:

Q: Determine the type of functions from R to R with necessary figure. i) f(x) = 5x + 7 ii) f(x) = (x² +…

A: (i) fx=5x+7 This function is state line and has roots is x=-75

Q: determine the most general function M(x, y) or N(x, y) so that equation is exact.

A: We have to find M(x, y) Or N(x, y).

Q: Consider the function y = 4ex + 7. What is the exact value of C in the interval [0, 5] such that…

A: We need to find value of C.

Q: Use the intermediate value theorem to show that f(x) = (e^−x^2)−x has at least one root in the…

A:

Q: Use the intermediate value theorem to show that f(x) = e −x 2 − x has at least one root in the…

A:

Q: Find points of discontunity of the function,where k is real number 1 f(x, y) sin(4 – x2 – y?) - -

A:

Q: Describe the domain and range of the function. f(x, y) = In(xy-1) Dor

A:

Q: At what points is the function f given by f(z) = x3 + i(1 + y) analytic? Explain.

A:

Q: 2. Sketch the graph of the function (a) f(x, y) = Vr² + y? (b) f(x, y) = Vx² + y? – 1 %3D

A: Given a. fx,y=x2+y2b.fx,y=x2+y2-1

Q: Express the function in the form f◦g. f(x)=sec(x2)tan(x2).

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.