Explain why the function is discontinuous at the given number a. (Select all that apply.) x2 - 4x if x # 4 f(x) x2 16 a = 4 1 if x = 4 f(4) is defined and lim f(x) is finite, but they are not X→4 equal. lim f(x) and lim f(x) are finite, but are not equal. X→4+ X→4- lim f(x) does not exist. X→4 O f(4) is undefined. none of the above

Q: Explain why the function is discontinuous at the given number a. (Select all that apply.) (2x² – 7x…

A: Introduction: A non-stop characteristic in arithmetic is one wherein a non-stop variant (that is, a…

Q: Analyze the function below. Which of the following is/are true? 8 f (x²) 184²8 x+1 as x → −1+, f (x)…

A: Given: To Find: To determine the true statements.

Q: Graph the piecewise function defined by (see attachment).

A: Given  The pricewise function is f(x) =3if  x≤-1x-2if x>-1.

Q: .6. Sketch the graph of f (x) = {3x+ 7, x- 3

A:

Q: Let f(x) a) f(a) = g(a) = 3x + 1. and g(x) = 2x. Determine values for a such that b) f(a²) = g(2a)

A: Given: fx=3x+1 and gx=2-x. We have to determine the value for a such that a fa=ga, b fa2=g2a.

Q: Which of the following functions has all of the following features? One negative x-intercept…

A:

Q: Explain why the function is discontinuous at the givennumber a . Sketch the graph of the function.

A: The function is given , fx=x2-xx2-1 ,  if x≠11,     if x=1 for a=1. To check the function…

Q: Let f(x) = 4 – x² . Find each of the following: f(8) – f(4) - 8 – 4 f(4 + h) – f(4) 3) II

A: (A) Given  f(x) = 4-x2 we have to find f(8)-f(4)8-4 Now f(x) = 4-x2 ⇒f(8) = 4-82 =4-64 = -60&…

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.