Consider the function f (2) = (2z+ 1) (z² – 1). - (a) What can be said about the continuity and differentiability of f at z = –1+ 2i? Continuous but not differentiable Continous and differentiable Differentiable but not continuous Neither continuous nor differentiable.

Q: Investigate the continuity of the following function S(2) = if z +0 if z = 0 (i) Is f(z)…

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

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Q: Find all differentiable functions f: R→R such that f'(x) = F(x + n) – f(x) n for all real numbers x…

A: As f'(x)=f(x+n)-f(x)n is true for all positive integers values of n thus substitute 1 for n in…

Q: The function f(x) is differentiable on (0, 1) and satisfies f(0) = f(1). However, its derivative is…

A: Consider the given function: Here the objective to check whether the given function contradicting…

Q: Use the second derivative f"(x) = x(x+ 1)(x-3) to determine where the function f(x) is concave down.…

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Q: Find the domain of f(z) the analytic function, graph on the z-plane.find the Re(f'(1)). f(z) = (z² +…

A: Given is the function f(z)=z2+1i. We need to find the domain of the function.

Q: If f:[-5, 5 ] to R is a differentiable function and if f'(x) does not vanish anywhere, then prove…

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Q: (@) Explain why f(z) = 5z"- 6+ Zcos z-z'e the function is entire?

A: To explain why the given function is entire, given function is: fz=5z4−6+zcosz−z3ez

Q: Let f(2) = x* – i(y + 1)°, (z = x + iy), (a) Determine the points where f is C-differentiable, and…

A: Given :-  let f z = x4 - i  y + 13 where z = x + iy (a) The points where f is ℂ - differentiable ,…

Q: Show that the function f defined by (x, y) = (1, –1) f(x, y) = { x2 + y (x, y) # (1, –1) x + y is…

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Q: f(x) is a function with the domain (-00, -7) U (-7, 3) U (3, 0), and the graph of given below (1.e.,…

A: Given, fx is a function with domain -∞,-7∪-7,3∪3,∞ and the graph of f''x is

Q: Investigate the continuity of the following function f(2)= if z +0 if z =0 (i) Is f(z)…

A: Calculate the limit:

Q: consider the function f, such that f and f are continuous for t > 0 defined by: 0<t<7 f(t)= -68t…

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Q: (B) Suppose that g(x) is a real analytic function such that: Find g(7) (-3) (derivative of order 7).…

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Q: x² + 1, x 1 Let f(x) = Is function f continuous at x = 1? Is functionf differentiable at x = 1?

A: Given :-  f(x) = x2+1 when x&lt;1  f(x) = 4-2x when x≥ 1  To find:- Check function continuous or…

Q: Let f(x) = (Vx + b² - b)/x, b > 0. What is the domain of f? (Select all that apply.) O (-∞, ∞)…

A: f(x)=x+b2-bx The given query is to find the domain of f(x) Also, to define the function such that it…

Q: Let f : R → R with f(x) = 3x² + 2. Prove that f is differentiable at the point –1 %3D

A: f(x) =3x2+2 f'(x) =limh→0f(-1+h) -f(-1)h        =limh→03(-1+h)2+2-3-2h        =limh→03+3h2-6h -3h…

Q: f(a) = ca + 4 if a E (-∞, 2] I ca -4 if a e (2, 00) if a E (2, ∞)

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Q: |x? +3x +1 ax + In x+b ,x21. „r<1; Let f(x) = If function f(x) is differentiable at point x=1, then…

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Q: (ii) Investigate the continuity of the following function f(2) ={ if z +0 if z =0 (iii) Is f(z)…

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Q: (f) Draw number line indicating where f" is + or - or 0 or dne (g) Find all inflection points (h)…

A: Given, f(x)=ln(x2+1)f'(x)=2xx2+1f''(x)=2(1-x)(1+x)(x2+1)2 (f) To draw the number line indicating…

Q: Prove and show complete solution: Let ƒ be defined on an open interval (a, b) and assume that ƒ has…

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Q: Consider the function f: R → R defined by f(x) = x³ – 3x + 2. Then (A) ƒ is increasing on the…

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Q: Let f: IR be a function. (a) Prove that if f is differentiable at some c I for which f(c) ‡ 0, then…

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Q: 8. Intro To Real Analysis

A: (i) For f(x)=x2+2x2+3x−3​, the function is a rational function. Rational functions are continuous…

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

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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…

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Q: Suppose that f(a) = f(b) = 0 and the second derivatives of f exist on the closed interval [a, b].…

A: Prove that ∫abx-ax-bf"xdx=2∫abfxdx.