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: (b). Show whether (*) is continuous at *=-2, if (3x-2 for x = -2 S(x)=. x? - 4 х- 2 for x * -2

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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: Let 4 – x² if x > 1 f(r) if x < 1 Determine whether or not f (x) is continuous at r = 1.

A: If left hand limit and right hand limit same, then f(x) is continuous at x=1.

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: Let f: A-XX Y be defined as f (a) = (f, (a). f2 (a)) each a A, Then f is continuous if and only if…

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Q: Show that the function f(x)=x|x| is continuous and differentiable at x = 0

A: To show that f(x)=xx is continuous at x=0 To show that limx→0xx=00=0 use piecewise definition for…

Q: Suppose that f(x) is a continuous function with f( – 1) = - 8 and f(3) = 8. Determine which choice…

A: Always true

Q: Determine whether f is continuous at a = -1.

A: Given- fx=x2-1x+1   if x≠-16           if  x=1 To find- whether f is continuous at x=-1 or not.…

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: (a) Prove that if æ > 3 and y > 4, then ry > 11. (b) Determine the range of f, if f : D → R, where…

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Q: Is the function 1 >-{ f(x) = √x x3 x < 0 0 ≤ x ≤ 1 piecewise continuous or piecewise smooth on [-1,…

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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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Q: The function f(x) = 1/ (x 4 + 6) is continuous for all values of x in R. %3D O False O True

A: We have to determine whether the given function is continous for all values of x in R or not.

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

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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.