10.2 Evaluate f(0,1) f(2) dz when f(z) is (i), (ii) (Rez)², (iii) z-2 (4-1), (iv) sin z. (Use the Fundamental theorem of calculus where applicable.)

Q: Consider the function f(z) = sin(z). (a) At what point (s) is f(z) differentiable? (b) At what point…

A: The given function is f(z)=sin(z¯). (a) To find: All Those points for which the function is…

Q: Consider the function f(r) whose second derivative is f(z)- 8z+10 sin(r). If/@)- 4 and f'0)-4, what…

A:

Q: Calculate the derivative using Part 2 of the Fundamental Theorem of Calculus. & 1² (520 - €) 30 dt =…

A:

Q: 3. Show that the complex function f(z)= cscz =1/ sinz satisfies the Cauchy-Riemann condition. Find…

A: The given function is fz=cscz=1sinz. A function fz=ux,y+ivx,y, satisfies Cauchy Riemann equations…

Q: Discuss the difference between harmonic and conjugate harmonic function. Also find the analytic…

A: The given problem is to discuss the difference between harmonic and conjugate harmonic function and…

Q: 2- Find the third derivative for əx3 for f(x,y) = sin) )+2 sin) sin)+3cos°) 8y3sinz s()+2sin()…

A:

Q: [59] Evaluate F.dr where F(x.y)3y'i+(x-4)j and C is the portion of y=(x-1) from .x-0 to r-3.

A: Please see the explanation below

Q: +. + 1 3. Exer. 33-36: Use right-hand and left-hand derivatives to prove that f is not…

A:

Q: (1) Are the following functions analytic: (a) f(z)=e* (cos 2y-isin 2y) (c) f(z) = cos x cosh y-isin…

A:

Q: Evaluate sec³ (0) tan³ (0)dē. ○ sec (0) - sec³ (0) + C ○ sec³ (0) + sec³ (0) + C O sec³ (0) + sec(0)…

A: Step 1:To solve the integral ∫sec5(θ)tan3(θ)dθ, we can use substitution and trigonometric…

Q: B3. (a) Let y be a function of x, defined implicitly by the equation x?y + y3 + x = 0. Find the…

A:

Q: 4. Evaluate each definite integral using the Fundamental Theorem of Calculus. (c) / (cos r – V3sin…

A:

Q: u(x, y) = -e sin x - 2e* siny. Find a harmonic conjugate v of u, namely a function v such that the…

A:

Q: dz (2) Suppose z is a function of x and and suppose cos(32) xyz?. Find in Y, terms of x, y, and z.

A: The given function is, cos3z=xyz2

Q: Prove that f(x)= sin(5x) < 5x on [0,x]

A: Take the help of derivative and try to prove the given statement in two cases.

Q: Check the continuity of the given function at the given c (or e's). (a) f(z) = { if 143 2-3 5 if z=3…

A:

Q: (6) If f(z) is analytic function show that: [v] + [0] =

A:

Q: (1) Let f(x) = 1,x > 0 with domf= R4+. Find the conjugate of function f(x). %3D

A: given fx=1x , x&gt;0 with domf=R++ claim- find the conjugate of function fx

Q: 5- Verify that the given function u is harmonic in an appropriate domain D. Find v(x,y), the…

A:

Q: Use the fundamental theorem of calculus to find F'(x) F(x) = r5x S COS I cos (v²) dv

A:

Q: c) Consider the function f defined by { f(x) = ex-1 X 1 if x ‡ 0 if x = 0 (i) Prove that f is…

A: