Select all of the following that need to be analyzed (or looked at) when deciding if a function, f (x), is continuous at x = c (where c is a real number). ✔lim f (x) exists. →C lim f(x) = 0 x→C You do not need to analyze (or look for) any of these conditions. Of (c) exists. ✔lim f (x) = f(c) x→C

Q: 2. Assume all given functions are continuous. If lim (f(x) - g(x)) = 10 and ƒ(5) = -8 x → 5 Find g…

A: The objective of this question is to find the value of g(5) given that the limit as x approaches 5…

Q: Determine if the function is continuous or not (using the definition) at the given z value. Then,…

A: Note:-Since you asked multiple questions, according to our policy we can answer only first question…

Q: Consider the following. ex if x < 0 f(x) = x+1 if x 2 0 (a) Determine whether the function is…

A: Part (a) For the function to be continuous at x = 0, we should have Left hand limit (LHL) = f(0) =…

Q: Let f(x) = -√√√x6 + 14 + x³ +1. Complete the tables below. Round all table values to four decimal…

A: The given function .The aim is to find the function value at the given points and find the limits…

Q: 1. Write a function of x, f(x), such that the following graph represents y=f(x).

A: Here we need to find a function for given graph in the question. According to the definition of…

Q: Construct a function that passes through the origin with a constant slope of 1, with removable…

A: This type of discontinuity can be removed just by defining f as that limₓ→ₐ = f(a) Here we have…

Q: The following is a step in the evaluation of the derivative of a function f(x) at a point x = 1…

A: