Show that the function f(2) = xy| is not analytic at the origin, even though C.R. equations are satisfied thereof.

Q: B) Estimate the next root of the function f(x)=x^3-x-1 using Muller method, let x0=1, x1=2, x2=1.5

A: Muller method: The Muller approach is applicable to any root-finding programme, but it is especially…

Q: Find a function f such that f ' (x ) = x 3 and the line x + y =0 is tangent to the graph of f

A:

Q: Find the quadratic approximation of f at x 0. - 1 4x f(x) = tan O A. Q(x)= 4x O B. Q(x) = 1-4x² O C.…

A:

Q: Show that the function f(x) = exp(−|x|) is not differentiable at x = 0.

A: We have given function fx=e-x As we know the modulus function is not differentiable at x=0.…

Q: e^x=3-2x

A: Given; ex=3-2x,(0,1)

Q: the function f is not differentiable at x=0.

A:

Q: Given the function f(x) = {2ª 2x x 2 which statement is FALSE at x=2? O The derivative from the…

A:

Q: Consider the function defined by y = g(x) = 3x² − 4x + 2. Determine the general equation of the line…

A: Given: Function g(x)=3x2 - 4x+ 2. Tangent perpendicular to the line y=-x2-2 .

Q: Show that g(x) = x|x| has an inflection point at x = 0, but gʻ"(0)

A: given function g(x) = xx

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

A: We can use application of derivative in order to solve the given problem.

Q: Use the Second Fundamental Theorem of Calculus to find F'(x). F(x) = 1 + t3 dt

A: To find F'x Fx=∫0xt21+t3dt

Q: · Use the definition of the derivative of complex function to show that f(z) is not dif- ferentiable…

A:

Q: Determine the linear approximation of f(x) = x² at x = 1. a. y= 2x +1 O b. y = 2x - 1 O c. y=- 2 x-1…

A: Given: f(x)=x2, x=1 To find: Linear approximation at given point.

Q: dy + ydx %3D 3x²y?dx,

A: Given differential equation is bernaulli's differential equation.,  and we can solve it by reducing…

Q: Find the value of c which satisfies the conclusion of Rolle's Theorem with the given f (x) =x- 3x,…

A:

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

A:

Q: Let be a real function of y=f(x) real variable implicitly defined by the equation 2xy−x2y2+ey=0.…

A:

Q: Show that the function given by f(x,y)= x² + 3xy is differentiable at every poin using the…

A: Introduction: Distinctiveness (differentiability) implies continuity. If a function is…

Q: Show that the given function is analytic in an appropriate domain. 2- y S(x) = Tr+2}* +3y² (x+2)*…

A: Please consider the handwritten solution.

Q: Show that the function y = x¹/², x > 0, is strictly concave

A: Given that y=x1/2 Differentiate both sides w.r.t x, y'=12x1/2-1y'=x-1/22 Again differentiate w.r.t.…

Q: 9. Show the function f(z) = 1 + 2i+2Re(z) is differentiable or not differentiable at any points.

A: Solution

Q: Find a function f such that f′(x)=2x^3 and the line x+y=0 is tangent to the graph of f.

A: Solved below

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: If f(z) is analytic function and u(x,y) = x3 - 3xy find f(z) %3D

A: Given that the real part of the analytic function f(z) is, u(x,y) =x3-3xy To find the analytic…

Q: Given that f(x) = 2x + cos(x) is a bijective function, find (f-')'(1)

A: The function f-1 represents the inverse of function f. Therefore, if f-1x=y then x=fy represents the…

Q: Verify that the real and imaginary parts of the follewing functions satisfy the Cauchy- Riemann…

A:

Q: Determine if f(x) is differentiable at x = 0 if

A: We will find out the required solution.

Q: Show that the function is differentiable at x=0 and find f'(0). f(x) = x2sin(1/x), if x is not…

A:

Q: Show that the function no-f 0, z = 0 f(2) = { – y* z#0 x2 + y? x² + y² is not differentiable at z =…

A:

Q: Let f(x) = 2 – x². Over the interval [0, 2], calculate (a) R4 and (b) L4

A: As per the instruction, we will be answering only the first question. For (1), For L4:

Q: (b) Show that the function f(z) = ez, z = 0 and f(0) is not analytic at Z = = 0, although C-R…

A: The given function is fz=e-z-4=1e1z4 To show: f(z) is not analytic at z=0 and f satisfies C-R…

Q: Show that the function f(z) = z is nowhere analytic on C.

A:

Q: Show that the given function is not analytic at any point but is differentiable along the indicated…

A:

Q: Let f(2)=u+iv be an analytic function. Given that u=v² show that f(z) is a constant.

A:

Q: 2. Use the First Fundamental Theorem of Calculus to differentiate the function -5x f(1) = | V1+ tª…

A: To differentiate the function by using first fundamental theorem of calculus f(x)=integration (x to…

Q: Prove that is a function f is harmonic =0, then - dx -Ldy =0.

A: Given function f is harmonic such that ∂2f∂x2+∂2f∂y2=0

Q: Find the linear approximation of the function at the give f(x.y) = 3x y at (- 6,9) O A. L(x,y) = -…

A:

Q: Suppose that f: R→R is a differentiable function, satisfying f(4)=3 and f(x) dx=6.

A: Given data: The first condition given is f(4)=3. The second condition given is ∫04f(x)dx=6. The…

Q: Use the Second Fundamental Theorem of Calculus to find F′(x).

A: It is given that,Fx=∫-2xt2-2tdt We have to use the Second Fundamental Theorem of Calculus to find…

Q: Show the function f(z) = 1+2i+2Re(z) is differentiable or not differentiable at any points.

A: Solution

Q: Use the Intermediate Value Theorem to show there is a root of the given equation in the specified…

A: Intermediate value theorem states that if “f” be a continuous function over a closed interval [a, b]…

Q: Show that the function d: RxR → R defined by d(x, y) = √x-y

A:

Q: Suppose that f(x)=xu(x), where u(x) is a differentiable function at x=2 such that u(2)=3, u'(2)=1.…

A:

Q: Under what conditions is a linear function f(x)=mx+b,m≠0, a linear function?

A: Here I am attaching image so that you understand each and every step.

Q: Show that the function f(r) = r* + + 7 has exactly one zero in the interval (-0, 0). %3D

A: Given function  fx=x3+4x2+7 Now we have to show that fx has exactly one zero in the interval -∞,0 If…

Q: "The function f(z) = x2 + i(2y + x) is nowhere analytic" is this statement true or false

A: If the function f(z) = x2 + i(2y+x) is analytic then it must satisfy Cauchy Riemann equation. Here,…

Q: Let f (x) = vx² – 2x + 2 + Vx² – 6x + 13. Find the point(s) on the graph of f at which the tangent…

A: See the handwritten solution

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.