4. Let's recall the definition of horizontal/slant asymptote. Let f be a function defined at least on an interval (c, o0) for some c E R. We say that f has an asymptote as r oo when there exist numbers m, bER such that lim [f(x) – (mx + b)] = 0 Notice that this includes both slant asymptotes (when m # 0) and horizontal asymptotes (when m = 0). Consider the following two claims: THEN lim f(x) exists. Claim A: IF f has an asymptote as x 00, f(x) exists, THEN f has an asymptote as r o. Claim B: IF lim (a) Prove that Claim A is true. (b) Prove that Claim B is false.

Q: Explain the differences between continuity and uniform continuity when f(x)=3x+7 shown on graph…

A: See the attachment

Q: 3 13 3 x f(x) = √₂² + 3x - 121 = 1² (√1 +²³2-¹) = (¹ + ¹ + 0 () − ¹) - 2 +0(1). |x| 1+ 1 x 1 2 x…

A: Here I am gonna show you how the limits were found:let's break downof the given function: f(x) =…

Q: Which of the following statement/s is/are true about the function whose graph is shown below? A fx)…

A:

Q: e functions f, g, and h from Exercise 2. an e-8 proof to support the fact that lim h(x) is equal to…

A: Here, in the question consider the functions f(x) = 3x+16x-12x+6, g(x) = {-10  when x =-6 3x-2 when…

Q: Sketch a graph of f(x) = -5 -4 -3 -2 -7 Clear All Draw: 5 4 3 2 1 -1 -2 -3 -5 wwwww 7 ' -3 x-1 P WWW…

A: Draw the graph as per condition

Q: 3.) The two graphs given in the sketch to the right are f(x) differentiable at x = 2. Find lim- x+2…

A:

Q: 5. Evaluate the following limits: (a) lim Inr xxx (b) lim In r →1-1

A:

Q: Consider the graph of the function /(x) below. Which of the following is true? 1. lim f(x)…

A: NOTE: Refresh your page if you can't see any equations. . as we can see the left-hand side of the…

Q: 14. f(x)= a. b. C. d. lim 2--1+ f(x)= lim lim lim 3(x-3)²(x+4) lim f(x) = f(x) =

A: see below the answer and explanation

Q: lim f (x) = +∞ x→1¯ lim f (x) lim f (x) = 0| lim f (x) – x + 2 = +∞ x→+∞

A: Horizontal Asymptote: As x goes to infinity (or −infinity) the curve approaches some constant value.…

Q: Direction: Check for the existence of the following limits. If it exists, determine the limit and…

A:

Q: I +b if x > 2 2) Suppose f(x) ={a if x = 2 if r < 2. (a) Find the value of b if lim f(x) exists. (b)…

A: Solution

Q: Below is the graph of a function f. -2 H

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.