18.13. Let f(z) be an entire function such that f'(z)| S/z|. Show that f(z) = a + bz2 with some constants a, bEC such that b<1.

Q: Let f:R-->R and suppose that |f(x)-f(y)| less than or equal to |x-y|^a for some a>1. Show that f…

A: Let f:R--&gt;R and suppose that |f(x)-f(y)| less than or equal to |x-y|^a for some a&gt;1. Show that…

Q: 5. Let f(x) = x-3x73. Use calculus to determine the critical numbers for the function.

A: Consider the  provided function, fx=x-3x23 Find the critical point of the critical point. Find the…

Q: Evaluate the double integral. / 4x2sin y²dA; R is the region that is bounded by y = x³, y = -x³, and…

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Q: Let f be a differentiable function such that 2 < f'(x) < 4 for all values of x. Show that 10 < f(12)…

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Q: Determine which of the points in the following list lie in the domain of the function f(x, y) =…

A: Let's find.

Q: Find all the analytic functions for ReZ=Im f(z)

A: Find all the analytic functions for ReZ=Im f(z)

Q: 10. Let F(x, y) = 1 + v4 – y². (a) Evaluate F(3, 1). (b) Find and sketch the domain of F. (c) Find…

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Q: Let f be a function defined on [15, 23]. Suppose for every x ≤ (15, 23) d da If f(16) = 44, find the…

A: We  know By definition of derivative  in interval a,b⇒f'x=limx→afx-fax-a

Q: Let f be a function that is continuous on [1,7] and differentiable on (1,7). Suppose 2 < f'(x) < 3…

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Q: 12. Let f be the function f(x)={ x² - 3bx+2; x2 For what value of b is f continuous at x = 2 ? (A) 0…

A: To find For what values of b is f is continuous at x=2.

Q: for t < -2 t+ 6 f(t) = for -1< t < 2 t2 -- t \3t - 2 for t 2 2

A: Given- ft=t2           for t&lt;-2t+6t2-t     for  -1&lt;t&lt;23t-2      for          t≥2   To Find-…

Q: 83. Let f(x) = In (1 – x²). (a) State the domain of f. (b) Find f'(x). (c) State the domain of f'.…

A: Since you have asked multiple question and have not specified any question in particular, I will…

Q: 13. Let f be the function defined by f(x) = xe*. What is the absolute maximum value of f? (A) 0 1…

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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: for If f (2) is a regular function of z, prove that f (2) 2 = 4 | f'(2) 1?. %3D ve I f12) 1? =4 |…

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Q: Let f be the function given by f(x) = 4x³ - 5x² + 6x + 7. What is the value of f'(-1)? 28 O 12 CO

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Q: Let the function f:R-->R be twice differentiable and suppose that f(x)≤0 and f''(x)≥0 for all x.…

A: It is given that, the function f:R--&gt;R be twice differentiable and suppose that f(x)≤0 and…

Q: 4.* (a) Let S = {1, 2, 3, 4}. Define F: SN by F(x) = x² for each x = S. What is the range of the…

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Q: Let f be a function defined on [11, 25]. Suppose for every x = (11, 25) d. dx -f(x) = 0. If f(12) =…

A: Given query is to find the value o f(24).

Q: Let f(x) = x-*,x > 0. Find the interval on which f is increasing or decreasing and find the local…

A:

Q: Describe the interval(s) on which the function is continuous. (TX) f(x) = sec

A: f(x)=sec⁡(πx4)

Q: We are given the following functions f : Z → Z × Z, f(x) = (x^2, x^3).  (a) Find images f({1, 2, 3})…

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Q: Draw the level curves for the function f(x,y) = x2-y. Show five level curves within the limits…

A: We shall use MATLAB to solve the above problem.We are using computer code so that it will be very…