„Show that the complex variable function below is differentiable analytic only at origin point? f(z) = |z|?

Q: Find the absolute extrema of the function on the closed interval. y = 5ex sin x, [0, π]

A: Solution:-Given functiony=5exsin x in [0,π]∴f(x)=5exsin xf'(x)=ddx5exsin x∴f'(x)=5ex cos x+5ex sin…

Q: Find the minimum value of ∣sin x + cos x + tan x + cot x + sec x + csc x∣ for real numbers x.

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Q: Determine whether the function f(x)=sinx2 satisfies conditions of Rolle’s theorem for the interval…

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Q: What is the necessary condition of analytic function ? Find the singular points of the function f (…

A: Necessary condition For a function f(z)=f(x+iy)=u(x,y)+iv(x,y) to be analytic is that it must…

Q: 3. Consider a function f(2) that is analytic in a domain that includes the real axis. When z is…

A: Given that,                 fz is an analytic function in a domain that includes the real axis .  We…

Q: Do the graphs of the functions in Exercises 39–44 have any horizontal tangent lines in the interval…

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Q: Qs:- Prove that fez) = cx-g') + ( are harmonic function of (xy) ,but not hormonic conjugates.

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Q: x sin if x # 0 Show that the function f(x)= is differentiable at x = 3D0 and f '(0)= 0. if x = 0

A: A  function is  differentiable at  point c if L f'c=R f'cwhere L f'c=limx→c-fx-fcx-c   =left hand…

Q: ex differentiable (analytic). You may wish to note the identity sinh(x + iy) = sinh(x) cos(y) + i…

A: Complex Differentiable or analytic: We know by Cauchy -Reimann eq f(z)=u(x,y)+iv(x,y) Then, the…

Q: Let f(x, y) = 3x2 – xy+ 2y2. Then an equation for the tangent plane to the graph of f at the point…

A: Given f(x,y)=3x2-xy+2y2

Q: True or false? Explain. The function f(x)=x² is invertible 1S

A: A function is invertible if we can establish one to one function such that two input can't have same…

Q: termine the absolute maximum and minimum values of f(x) = cos²x-cosx the interval 0≤x≤ 2π.

A: Given that fx=cos2x-cos x, x ∈0, 2π To determine:  Absolute minimum and maximum. Needed formulae:…

Q: S: sec h udu = tan"(sin h u) + C -1

A: Follow the procedure given below.

Q: 21. Let Sech u = 3/5 , determine the values of the remaining five hyperbolic functions.

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Q: Use Theorems 1-5 to show that the function zs continuous. f(x) = x + sinx

A: Consider the given function: fx=x+sinx As we know, sum of finite continuous function is continuous.…

Q: sec³ x sin x dx (Hint: factor out cos? x) Vcos? x + sec x

A: Consider the provided integral, ∫sec3xsinxdxcos2x+secx Solve the integration by u substitution…

Q: Integrate to find F as a function of x, and demonstrate the Second Fundamental Theorem of Calculus…

A: Integral is F(x)=∫4xt32dt

Q: What does it mean for a function ƒ(x, y) to be differentiable? What does the Increment Theorem say…

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: Find the approximation for the Green's function of the one-dimensional acoustic wave equation in the…

A: Given function is, cx=aebx Here, a>0 and it's constant here we have to see the effect of b so,…

Q: f(x)=\arctan (1-x),[0,1]

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Q: -2,2] R, then show that the function sin for x 0, f(x) = for x 0, aly continuous.

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: what the derivative of the function of complex numbers f(z)=(z3 - i)2

A: Given function, f(z)=z3-i2

Q: Prove that the function (z*)2 1리 > 0 0, z = 0 f (z) = is not analytic at z = 0 by calculating all…

A: Calculate the derivative of fz at z=0.  f'0=limZ→0fz-f0z-0       =limZ→0z*2/z-0z-0       =limZ→0z*z2

Q: . Use the second-derivative test for local extrema (: extrema for the function. Identify whether the…

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Q: Let f(x)=/1-x²,A=(-1,f(-1)),and B =(1,ƒ(1)). Find a tangent line to f on the interval (-1,1) that is…

A: If tangent parallel to given secant line then their slopes are equal

Q: snip

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Q: 2e 1 sec (x). -dx SEC | le

A: Given query is to evaluate integral using fundamental .

Q: sin (r) -dr. R nvoke to integrate even powe

A: An integral is given by, I = ∫Rsin2xx2dx. The objective is to evaluate and state the identities that…

Q: What is the directional derivative of the function f (x, y) = 2xy- 3y2 at point po- (5,5) in the…

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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: Find the absolute extrema of the function on the closed interval.

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Q: Find all points of inflection and discuss the concavity of the function f(x)=-sin x+cosx on the…

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Q: GrRve the domnin f n(x)= -9-4x|usq iaeoul.ntaton

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

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Q: f) = In(tanx) -1 %3D

A: ddxlnarctanx

Q: The curves f(x) = x² – 3x + 2 and g(x) = - z+5 intersect at the point (-1,6). ㅠ Find the acute angle…

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Q: Integrate to find F as a function of x, and demonstrate the Second Fundamental Theorem of Calculus…

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Q: 4) Find direction derivative f(x, y) = x2 -3xy at the point (-1,2) in the direction 0 %3D 6

A: The directional derivative of a function f(x, y) is given by Du.fx,y=fxx,ya+fyx,yb where u.=a,b is a…

Q: i. State and proof the necessary and sufficient condition for analyticity of complex function.

A: Here we have to state and proof the analycity of f(z).

Q: EXERCISES 2: Find the derivative of the function at Po in the direction of A. 1. f(x, y) = 2xy –…

A: Ae per our guidelines we are supposed to solve only one question. For the solution of the first…

Q: Find the derivative of f(z) = In(z -+ O (A) f'(2) = 2² – 3z + 2i). | --2 V:-3:+2; 1 AB) ƒ'(2) = V-3:…

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Q: what the derivative of the function of complex numbers f(z)=(z3 +i)2

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Q: Find the directional derivative of f at the given point in the direction indicated by the angle 0.…

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Q: 2 What are the zeros of f(x) = 12 sinx-6 on the interval [0,2x]? %3D

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Q: Find a point 2o where the function f (2) = (z – 12 – 12i) (z – 12 – 12i)differentiable. What is the…

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Q: Real part of f(z) = z +i-1 is:

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Q: Olet of all real numbers R としメ) e 1R RIy2メ Show that fis function

A: Introduction: A function is an expression, rule, or law in mathematics that defines a relationship…

Q: tan-(t) Given F(x) = dt, evaluate F(0) and F'(0). 1+sin(2x) 1+ et-1

A: It is givne that, F(x)=∫1+sin-1(2x)1tan-1(t)1+et-1dt ......................................... (1)…

Q: QI: If u(x; y) = eY sin x - x. Show that u(x, y) is harmonic and find its harmonic conjugate v(x, y)…

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Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.