Suppose that the function f: [0, 1] in R is continuous and thatf(x) > 2      if 0<=X < 1.Is it necessarily the case that f ( 1) > 2?

Q: Define g(-5) in a way that extends g(x) = x² - 25 x + 7x + 10 to be continuous at x = -5.

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Q: f: Z4 → Z5 f([a]4) [39]s if a > 0. =

A: Introduction: A well-defined function is a function that is unambiguously specified by its…

Q: Define 1 if x 2 Determine the values of a and b such that f(x) is continuous for all x.

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Q: Consider the following piecewise defined function ae*-b, x < 0 ax² +b, 0≤x≤2 a(x − 3)³ + b(x − 4) +…

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Q: (3-x, xs1 Consider the function given by f (x) = Is the function continuous, %3D x -x+1, x>1…

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Q: Suppose that a function f is analytic on the interval (1, 10). Suppose that another function g is…

A: Given  Suppose that a function f is analytic on the interval (1, 10). Suppose that another function…

Q: Show that the function Arg(z) is not continuous on each point of the non-positive real axis.

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Q: Consider the function f with domain (-2, : 3|22 – 1| if – 2 < x < 1 2x2 + 2x – 4 f(x) = 3 if x = 1…

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.