4. For the given function, f, determine if the function is discontinuous at a given point. State which of the continuity falls or state the function is continuous at x = а. (3+2x, x<0 0 < x < 1 f(x) = a = 1 x, %3D -x2 x 21 The function is lim f (x) does not exist continuous at x = 1 O Option 1 Option 2 lim f (x) # f(1) f(1)does not exist x-1

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: 4. Determine whether the functions f are continuous at given points: x+2 S(x) ={ x +x-2 0, x=1 at x…

A:

Q: ( 10 – a x2 if 4 Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(x)…

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

Q: 5 if x - 3 Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(x) = I+…

A:

Q: Determine if the following piecewise-defined function is differentiable at the origin. 4x - 6x° - 1,…

A: topic - derivatives

Q: 8) Suppose if x 20 f(r) = if x < 0. Identify a function g with domain R such that lim(f +g)(x)…

A:

Q: Q 6 Show that the function f(x) = 1+x³ -V1 – x2 is continuous on the interval [-1, 1]. (HINT: show…

A:

Q: Consider the piecewise defined function x² + 2x – 1 if x 0 ° Which of the following statements is…

A: As we know that,  the function fx is continuous at a point  x=a if the left-hand limit is equal to…

Q: - 3 – x + 2 if x - 4 Calculate the following limits. Enter "DNE" if the limit does not exist. lim…

A: Topic = Limits

Q: Suppose that f: R→R is a continuous function, satisfying f(5)=8. What is the value of the limit lim…

A:

Q: 4. For the given function, f, determine if the function is discontinuous at a given point. State…

A: fx=3+2x,  x≤0x,         0&lt;x&lt;1-x2,      x≥1 Now, f1=-12    ∵fx=-x2  when x=1=-1 Left hand limit…

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: Based on the given values, is the function continuous or not? If not, select the condition which is…

A: In the given question we have to tell such function which satisfies the given three property and and…

Q: ) Find the value of k that makes function continuous at ¤ =4 f(x) = { | 2x +7 > 4 6x -k < 4 (i) If…

A:

Q: 3. is a type of discontinuity when the lim and lim f(x) = M where L# M and either f(a) does not…

A: Discontinuity 1: When the limx -&gt; a- f(x) = L and limx -&gt; a- f(x) = M, where L ≠ M and either…

Q: 10. Determine which of the following limits exist and does not exist. a. b. 2 - 2 3x - 9 lim 25 * +5…

A: Note:- As per our company guidelines we are supposed to answer only first three sub-parts. Kindly…

Q: Suppose we want to determine whether h(x) is continuous at x = 3. So far, we are given the two…

A: We have, limx→3-hx = 6 h3 = 6 To evaluate: The additional information needed which will allow us to…

Q: Suppose that f(x) 0 for all a in the interval (-1,1). If lim f(x) = L, then %3D L> 0. For those who…

A:

Q: (- 4 - x) + 4 if a - 5 | 2x + 14 Let f(x) %3D if x=D - 5 Calculate the following limits. Enter "DNE"…

A:

Q: 2. For the given function, f, determine if the function is discontinuous at a given point. State…

A: Given function is fx=xx. To find whether function is continuous at x=a, where a=0. Solution:   we…

Q: Let y = f(x) be a continuous function on R. If both of the limits lim f(x) = L1 and lim f(x) = L2…

A: From the given information, function f(x) is continuous and above limits exist and equal. Now…

Q: 4. A function g is defined to be: (b) If we chose c as in part (a), what must K be so that g is…

A:

Q: 1. Determine whether the function f(x) = x2 + 6x + 9 is continuous at x =-= Sketch its graph…

A: Consider the provided function and the point, fx=x2+6x+9,   x=-2 Evaluate the provided function at…

Q: 1. Determine whether the function ƒ(x) = x² + 6x +9 is continuous at x = -2. Sketch its graph…

A: Here, the given function is: f(x)=x2+6x+9 which is a polynomial function. To determine the…

Q: Suppose that for a function f, f(3) is not defined. Also suppose that lim f(x) = 2 and lim f(x) = 2…

A:

Q: . Suppose a state's income tax code states that tax liability is 12% on the first $20,000 of taxable…

A:

Q: Consider the function f(x) whose graph is f(5) %3D 6. lim f(x) 4 lim f(x) %3D エ→5 3 lim f(x) 20 I-3+…

A:

Q: a. The number L is the limit of f(x) as x approaches c if given any ɛ > 0, there exists a value x…

A:

Q: Use the limit definition to find the slope of the tangent line to the graph of f at the given point.…

A:

Q: 2 – x – x2 if x 5 Calculate the following limits. Enter "DNE" if the limit does not exist. lim f(x)…

A:

Q: Is the given function continuous at a=7 ? x2-49 if x=7 f(x)=. x-7 if x=7 Solution: f(a) lim f(x) =…

A:

Q: Determine if this function is continuous at z = -1 f(1) I -1 where f (x) = I+2 and g (1) = - +3z +…

A: NOTE: Refresh your page if you can't see any equations. . here we want the left-side limit at x=-1…

Q: 2. a. Draw a graph with the following characteristics: lim f(x) = 3 X-2* lim f(x) = 0 X-→2 f(2) = 3…

A: The graph has the following properties,limx→2+f(x)=3limx→2-f(x)=0f(2)=3limx→-1f(x)=-2f(-1)=1

Q: 2 — х — г? if x 5 - Calculate the following limits. Enter "DNE" if the limit does not exist. lim…

A: Here we will find the given limits,

Q: Is the discontinuity at x= 0 in the given graph removable? Explain. 101 8- 41 -10-8-6-4 246 8 10…

A: Given, graph of a function having a discontinuity at x=0

Q: Question 4

A: The condition which should be satisfied for continuity,

Q: 10 – x – x2 if x 4 - Calculate the following limits. Enter "DNE" if the limit does not exist. lim…

A: Given that fx=10-x-x2if x≤42x-5ifx&gt;4   (1) Find limx→4-fx Left hand limit: For x&lt;4 ,…

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: 1. Consider the given piecewise function f(x), find the limits at the given values. State if the…

A:

Q: 8) Suppose if r 20 if r < 0. f(r) = Identify a function g with domain R such that lim(f+g)(x) exists…

A: The explanation is as below

Q: 2. Use Squeeze Theorem to find lim, x f(z), if for all z > 4 Ge² – 15 < {r) f(x) < VE-2 2e

A:

Q: 2. The function is called to be lim f (x) = f(a). エ→ロ 3. is a type of discontinuity when the lim…

A: Fill in the blanks: 2. The function is called to be continuous at point "a" when the limx→afx=fa.

Q: Is the function given by 1 g(x) = 4*+1, for x 8, continuous at x= 8? Why or why not? Select all that…

A: We have to check

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: Show that the function is continuous at the given value. f(x) = 3x, c = 2 The function f(x) is…

A:

Q: 1. Determine whether the function ƒ(x) = x² + 6x +9 is continuous at x = -2. Sketch its graph…

A:

Q: A function y = f(x) is defined and continuous for all x. This function satisfies all of the…

A: Given that the function  y=fx is defined and continuous for all x. Solution (a): According to the…

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

A:

Q: x+4 Which will prove that f(x) is continuous at C= -4? x2+16 1. f(-4)=0 II. lim f(x)=0 III. f(x)=…

A:

Q: ,if x> -3 Given the function f(x) =' 3 ,ifx S-3 is continuous at x=-3

A: A function                      fx=x2-9x+3,   if x&lt;-33,             if x≤-3 We have to answer the…

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.