General Direction: Handwritten solution is a must. Kindly indicate all the necessary solutions. I. Given: 2 +x if x < -1 [x – 1] x² – 4x if – 1

Q: f(x) : ²+4x-5 a+5 c = - 5

A: The objective of the question is checking the continuity of the given function at given point.

Q: Use the following information for Questions 4 and 5. f is a continuous function with a domain [-3,…

A: (5) Given that , fx=3,          -3≤x≤0-x+3,    0≤x≤6 -3,          6≤x≤9 and gx=∫-2xftdt Find gx in…

Q: The function f(x) is defines as  f(x)=e^(-1/absolute value of x) if x do not equal to 0;         0…

A:

Q: is continuous or discontinuous at x = -4 using the three step continuit x + 6 x -4

A: We have to check continuity  of function

Q: Given the function, g(x) x 2 a. Determine the possible points of discontinuity. b. Discuss the…

A:

Q: 3. J Use the definition of continuity and the properties of limits to show that the function is…

A: As per bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: 1. For what value of k is the function h(x) continuous on the whole real line? HINT: Use definition…

A:

Q: For what values of a and b is ax + 2b, g(x) = {x + 3a - b, 0 2 continuous at every x?

A:

Q: Determine the whether the function is continuous at x=-2. Justify your answer 2x+7 if xS-2 using the…

A:

Q: Let 1, if-3 <x s2 f(x) = %3D 4-x, if 2 < x<4 Without graphing, is f(x) continuous at x 2? Clearly…

A:

Q: Given the function, g(x) 3 x 2 a. Determine the possible points of discontinuity. b. Discuss the…

A:

Q: Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable?…

A:

Q: Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable?…

A:

Q: Use the definition of continuity and the properties of limits to show that the function is…

A: We have to use the definition of continuity and the properties of limits to show that the function…

Q: For what values of a and b is -2, xS-1 f(x) = ax - b, -1 <x<1 3, continuous at every x?

A:

Q: x² – 16 f (x) = x( x 2(х — 1)°(х — 2) : о 1)8 (x – 2) : 0 - -

A: If the given function is equal at LHL and RHL at x=3 then the given function is continuous at x

Q: Consider the following. Sx² - 3, 3x + 1, x -1 Describe the interval(s) on which the function is…

A: In the case of piece wise defined function check the continuity in each interval and also at end…

Q: Verify that the Intermediate Value Theorem applies to the indicated interval and find the calue of c…

A: Given function is

Q: Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable?…

A: Given :             f(x) =1(4-x2)

Q: let f(x) = |x| / 5x , which of the following is actually true? a) f is defined at 0  b) f is…

A: The given function is: f(x)=x5x

Q: Use the definition of continuity and the properties of limits to show that the function is…

A: A function is continuous in an interval if is continuous on every point of the interval. Now, a…

Q: -x ifx1 function f. Where is f discontinuous? Justify your answer using the definition of…

A: We first make a table for the function x -4 -1 0 0.5 1 2 3 4 y 2 1 1 0.5 DNE 1 4 9 Then we…

Q: I'm having trouble understanding the continuity questions, please see the attached screen shot.

A: We find left and right hand limit at x=0.Left hand limit = 1

Q: 4. Find the values of x-values (if any) at which f is not continuous. Which of the discontinuities…

A:

Q: Consider the following. S-3x, f(x)={2 - 2x+ 9, x > 2 Find the x-value at which f is not continuous.…

A: We will find the value of x at which the f is not continuous and whether the discontinuity is…

Q: Consider the following f(x)= 2/4-x2 Find the x-values at which f is not continuous. Which of the…

A:

Q: 1. f(x) 2. f(x) = 3. f(x) x² - 4x X 2x x²-9 x² x-2 ; C = 0 -4 ; C = ; C = 2

A: Since you have posted multipart questions i can do first three subparts as per our company…

Q: S(x) = 7x* – 1x* +2. | Use interval notation to indicate where f is continuous. Domain of…

A:

Q: Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable?…

A: Given function is

Q: Let f be the function defined as follows: [3-х, for x <1 f(x)= {ax2 + bx, 5x-10, for 1<x <2 where a…

A:

Q: ((4— х)2 х 1 continuity at the indicated test point. If it is discontinuous, specify the type of…

A:

Q: Answer the following True or False: If f(x) is defined and continuous on the open interval (a,b),…

A: The Extreme Value Theorem states that  If f(x) is defined and continuous on the closed interval [a,…

Q: (2) Determine if each function is continuous at the given value of a. Justify your answers using…

A:

Q: х — 3 - 40. f(x) x2 – 9 - x + 2 41. f(x) x2 — Зх — 10 - - x – 1 x2 +х — 2 - 42. f(x)

A: To find The x values at which the function is discontinuous

Q: Q2) Discuss the continuity at x=2. When: x> 2 X = 2 x< 2 Зх + 1 f(x) = } x? + 3 %3D 2х + 1

A: Our objective is to discuss the continuity at x=2.

Q: Use the e – 8 definition of continuity to prove that each of the following functions is continuous…

A: use the ε-δ definition of continuity to prove that each of the following functions is continuous on…

Q: b) Discuss the continuity conditions of the function- f(x) which shown in figure at x= 0,x = 1,x= 2…

A:

Q: Find a value of the constant k, if possible, at which kx2 f(x) = x+k x> -7 is continuous everywhere.…

A:

Q: 3. Use the definition of continuity and the properties of limits to show that the function is…

A: As per our guidelines we are supposed to answer only one question i.e. the question no (a). For the…

Q: What type of discontinuity is present in the function 3x – 2 if r 2 O The function has a removable…

A:

Q: 4. Discuss the continuity of the function f at x = 0. Iff is discontinuous at x = 0, is it…

A:

Q: 3. Consider the function h whose graph is given below. a. Is h continuous at 1 = 0? Justify your…

A: Given,

Q: B. so, find f'(2). If not, explain why not. It can be shown that f is continuous at x = 2. Isf…

A:

Q: Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable?…

A: Given: fx=1x2+1 To find discontinuities find the value of x at x2+1=0 x2+1=0x2=-1 But there exists…

Q: Determine the continuity and, if discontinous, the type of discontinuity for the function…

A: Given query is to find function is continuous or not at x = -1.

Q: I'm stuck on this question and I don't know how I should be approaching this. What should I do?

A:

Q: f(x) = 3x - 5x² 1. c = 2

A: Given: fx=3x-5x2  ; c=2   The function will be continuous at x=c when, limx→c-fx=limx→c+fx=finite…

Q: Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable?

A: Here given function as fx=x+2x2-x-6orfx=x+2x-3x+2orfx=1x-3

Q: For what values of h and k is h+2x , 15 x52 -2 < x<-1 2< * 2 - Continuous at every x ? 2x2 - 2x-4,…

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.