f(2) = 4 and f(3) = 3. With this information, can you determine whether there exists a real number c such that f(c) = 8? Why or why not?

Q: (3-х, х <2 +1, x 2 2 B. Is the function h(x) continuous at x-2?

A:

Q: 1. Find the numbers for x where the function below is not continuous. Explain what type of…

A: Here the given graph

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

A:

Q: On what domain is the function f(x) = 3 + V5x – 20 continuous?

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Q: A function f which has an absolute maximum and an absolute minimum should be continuous. Select one:…

A:

Q: Let f(x) be a continuous function. If f(c) is an absolute max or absolute min, then c is unique. O…

A: Given,  fx is a continuous function fc is absolute max or absolute min , then c is unique.  We have…

Q: Is the following statement correct? If the function is continuous on R then the constants a and b…

A: It is not necessarily correct that every continuous function on R take the value 2&amp; -2…

Q: Show that the following function is continuous or discontinuous at. f(x)=x2+x-6/x2-4

A: The given function is

Q: Determine whether the following function is continuous at the given point z За? + 14г — 5 1 f(x)= 3x…

A:

Q: Find constants a and b such that the function 3– bx, if x>-2 f(x)=- -1, if x=-2 ax – bx, if x<-2 |…

A: Given query is to find the value of a and b.

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

A:

Q: (x² + 8, if x4) Consider the function f(x) = Find the value of B such that f (x) is continuous at x…

A:

Q: Justify that 12-21-3 if x + 3, f(x) = 4 I-3 if x = 3

A:

Q: 1. Find the numbers for x where the function below is not continuous. Explain what type of…

A:

Q: 1. Find the numbers for x where the function below is not continuous. Explain what type of…

A:

Q: If f is a function that is continuous on the open interval (1, 4), then f is continuous at x = 3.…

A: Given: If f is a function that is continuous on the open interval (1,4), then f is continuous at…

Q: Determine whether the following function is continuous at the given point x = 3 За? + 17х — 6 1 -…

A:

Q: Provide an example of function f: R → R which is continuous at exactly one point and discontinuous…

A:

Q: Find the value of the constant a that makes the following function continuous on (-∞, ∞). 5x³ + 5x²…

A: We need to find a value that makes the function continuous.

Q: ii) f(x) = x*-1 %3D x²-1

A:

Q: the following function is a continuous function at x=2 امرفق x² +x-6 x+ 2 x) = x2 - 4 x = 2

A:

Q: ample 23: Show that the function f(x)=1-1-x is continuous on the interval [-1. 11.

A: A function y=f(x) is continuous in an interval [a,b] if it exists for every x∈[a,b] In other words a…

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.