Problem 4. 10. Show that (a) the function f(z) = Log(z - i) is analytic everywhere except on the portion <0 of the line y = 1; Log(2+4) (b) the function f(z) points ±(1 - i)/√2 and on the portion = is analytic everywhere except at the -4 of the real axis.

Q: The derivative of f(z) = Log(2iz – 4 + 6i) at z = -3 + 4i is %3D Log(-12). O 2i -12 None of them O…

A: We have to find Derivative using definition and L'Hospital Rule.

Q: 1 Po(x) = v2 3 P1(1) = : %3D "V 2 PĄ(2) = (3=² – 1) V P3(x) = ; (5x³ – 3r) /5 Write down the…

A: We will find out the required values.

Q: Determine x[4] for the given Difference Equation 2x[k + 2]- x[k + 1]+ x[k]= k^2 x[0] = 1 x[1] = 3

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Q: 3. Consider the function +R where f(r)= log,(2-52). (a) Find the rule for f-. (b) State the range of…

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Q: if f(x)={ -3x       for x -1  find f(-2)  a. -6 b.9 c.6  d.-1 e.0

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Q: Consider the following functions Step 3 of 4 Find/gXI). Answer /=(-24(1-1). (4,4)) 5 Points and x=…

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Q: Find the derivative of the function. Ax) = 6x (9 - 8x)* O (- 12x) (9 - 8x)' (6x- 9) O (-181 )(9- 82)…

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Q: Write 1 true and-1-false for your answer. Let A= Answer: (13) B-(23) 0-(63) (37)- C= , Is a linear…

A: We need to see if the given matrix  is a linear combination of matrices A,B,C Now,…

Q: Determine whether the functionf is one-to-one by examining the sign of f' (x). (a)ƒ(x) = x³ + 9x2 –…

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Q: 1. Assume that the function f is a one-to-one function. (a) If f(2) = 5, find f-(5). Your answer is…

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Q: 1 +Vx+1. (1–log (9-x)) Find the domain of (a) (-,9) (b) [-1,9) c) [-19] (d) (-1,9)

A: Domain of the given function is given by

Q: If a = 1 − v^2 and both x and v are zero when t = 0, show that x = −1/2ln(1-v^2) and hence find v^2…

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Q: vertical asymptote(s): horizontal asymptote(s):

A: Since multiple subparts are asked, I am answering first 3 subparts

Q: Find f. f ″(x) = 8x3 + 5,    f(1) = 5,    f ′(1) = 4

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Q: Find the second derivative of x-5x² + x 0. A. 10x-5 B. 6x10 C. 3x + 10 3x² - 5x D. Given the…

A: We need to calculate the derivatives of the given functions:

Q: Find the slope of the graph of the function x2+y2=xy+1/4 at (1/2 , 1/2)

A: Given function is Differentiating both sides with respect to x, we get

Q: The point Q (-4,7) lies on the function f(x). Suppose f(x) is transformed according to: y=-3 f…

A: The transformed function is given as , y=-3f0.5x+3+5 Determine the x-coordinate of the transformed…

Q: Suppose that ƒ(x) and g(x) are two functions and we know that: ƒ(-3) = 2 g(-3) = 5 ƒ'(−3) = −1…

A: Suppose that fx and gx are two functions and we know that,  f-3=2g-3=5f'-3=-1g'-3=-2 To find the…