2. By drawing a graph illustrate an example of a function f(x) such that it satisfies these three conditions: lim,→1- = 2, lim→1+ = -1 and f(1) = 0.

Q: 4 if x 2 Find the value of c such that lim f(x) exists. x→2

A: Given the piecewise function :

Q: 1. Let f(x) = 3² – 2x + 1. Compute lim (x)f – (4 + x)f 0+-4

A:

Q: Determine whether the function x2 + 2 x > 2 f(x) = x = 2 is continuous at the 4х — 2 x < 2 given…

A: First of all we will find the left hand limit at X equal to 2 and then find the right hand limit X…

Q: 2) Show that the_lim. 1) xy2 lim (x,y)→(0,0) x² +y²

A:

Q: 1. Use the definition to show that x² - y² lim (x,y)→(0,0) x² - y² = 0.

A:

Q: Consider the graph of y = f(x). 4- -8 -7 -6 -5 -4 -3 -2 -1O 2 3 5 -2 For infinite limits, use 00 = 0…

A: As per our guidelines we are supposed to answer only first three parts. kindly repost others part as…

Q: Determine whether the shown statement makes sense or does not make sense, and explain your…

A: The functions whose graphs can be drawn without lifting the pencil off the paper is a continuous…

Q: 2. Write the equation of a function that is discontinuous at x=5, but lim f(x) exists, and is…

A:

Q: 4-Find the limits of the following x -1 1. lim Vx +3 - 2 Vx² +2 2. lim X+0 3x –6

A:

Q: 1. Evaluate the limit for the graph lim f (x). x→1" f(x) 51 4- 3 2 1- -3 -2 -1 1 2 3 4 -1 а. 1 c.…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: For the function f(x) (X^2-3 if -3 ≤x2 C) is f continuous at x=2? D) does lim f(x) exist at x->4^-?…

A:

Q: Evaluate lim as x approaches negative infinity 3e^2x + 4e^-x / e^2x - 2e^-x .

A: Limit of a function determines the continuity of a function. Three types of limits exist, one is…

Q: 2x+1 if x < 2 Let f(x) = x²-1 if x ≥2 Determine the one-sided limit lim f(x). x 2+

A:

Q: Determine whether the statement makes sense or does not make sense, and explain your reasoning.

A: Let us consider limx→a-f(x)=A and limx→a+f(x)=B We have, A is not equal to B. When x gets close to…

Q: Verify the limits in a given equation below. (2х-4)2 lim X→3 x+1

A:

Q: Let f(x) = x/(x + 1). What is lim, »f(x)? How large does x have to be so that f(x) > 0.99?

A: Given:            fx=xx+1 Find: limx→∞fx=limx→∞xx+1

Q: lim 극 et – 1 x-1

A:

Q: If a function is defined at a, but lim f(x) does not exist, how is x→a this shown on the function's…

A: If the limit of a function f(x) does not exist at a, then the function is not continuous at a and…

Q: 2x+1 if x 2 Determine the one-sided limit lim f(x). x-2- 2

A: The given function is:

Q: -f(x): a. lim

A: We'll answer the first question only since the exact one wasn't specified. Please submit a new…

Q: b. f(3) = 2 and lim f (x) does not exist.

A:

Q: draw the graph of a function on [0, 5] with the given properties.

A: Removable discontinuity at any point (a) of domain of function (say f(x)) is define as Graphically…

Q: Suppose a function f satisfies f(3+h) – 2 lim = 7. Find an equation for the line tangent to the…

A: Let

Q: 1. Consider the function f(x, y) = 2y (a) Show that lim (x,y)(0,0) f(x, y) does not exist by using…

A: Note: if a limit exists at a point,it must be the same limit along any path approaching that point.…

Q: Sketch a possible graph for a function, f(x), where f(3)=1, f(x) is not continuous at x = 3, and lim…

A: A function is said to be continuous at a point, if it is defined at the given point, its limits…

Q: 4. Evaluate the limits of the following functions: a) limsinx x-0 sin x-tan x 6 b) lim x-2 x2+2x-8)…

A:

Q: 14. (a) Use a graph of 1(6) = (1- 2)" f(x) = to estimate the value of lim f (x) correct to two…

A:

Q: * + 2, if x 0' (a) Find lim f(x). (b) Give a simple reason why f is discontinuous at 0.

A:

Q: i. Calculate the following limit: 2x|x – 1| lim - x-1 x-1 ii. Determine the limit of f(x) when x…

A:

Q: 2x-1 2. lim X-2 \3x+4,

A:

Q: 2. Create a graph that satisfies the given conditions. im f (x) = -∞, lim f(x) = ∞, lim f(x) = 0,…

A:

Q: Find the limit. lim (2 – x)3 tan(a) x→1

A: limit

Q: 1. Complete the table of values to determine the limits of the function. f(x) = = -1-0.5 -0.1 -0.01…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Suppose that f(x) = 2cos (n/3 x) and the graph of g(x) is given by: y = g(x) 2 1 -5 -4 i ż 3 4 5 x…

A:

Q: From the graph: (x) is discontinuous at x= 3 because of (a) Lim f(x) = f(3) (b) Lim f(x) doesn't…

A: According to graph at x = 3

Q: 1. Sketch the graph of a function with the given properties. lim f(x) = 2, lim f(x) = -, lim f(x) =…

A:

Q: . What is the point discontinuity of the x² – 1 lim x→-1 x +E 1

A:

Q: 1. Sketch a graph of a function f(x) with the following properties: f(-2) = 0, ƒ(2) = 0, lim_f(x) =…

A:

Q: Determine the following limits at infinity. lim x-11 xS-0

A: limx→-∞x-11

Q: (6) Draw the graph of a (a) function ƒ satisfying Y S(1) = 2, S is continuous at 1. What is lim,→1…

A: f(1)=2f is continuous at 1

Q: The function f(x) of the below graph is discontinuous at x = -1 because: a) f(-1) does not exist b)…

A:

Q: 3. If f and are continuous functions with f(3) 4 and lim 2f(x)-9(r)3D5, what is g(3)?

A: To evaluate the value of the function

Q: Consider the function - x2, x+1 f(x) = 2, x = 1 O Graph the function f(x). O Find lim,1-f(x) and…

A:

Q: 6) Find lim f(x). X>T/2

A: Given graph we have to find limx→π2f(x)

Q: Determine a reasonable estimate for lim hx x-1 3 -5 -4 -3 -1 3 5 2. 1 4. 1. 1. 2. ee

A:

Q: . For a function f, suppose lim f(x) does not exist because values of f(x) oscillate between two…

A:

Q: What conclusion about f(x) can be drawn from the equation lim-a+f(x) = f(a)?

A: Given that limx→a+f(x)=f(a)

Q: f(0) = 1, f"(x) < 0 for x # 0, lim f'(x) = +0, lim f'(x) = -00

A: