It is possible that functions f and g are not continuous at a point x0 but f+g is continuous at x0. Select one: True False

Q: What three conditions must be met for a function ƒ to be continuous at the point (a, b)?

A: Continuity at points: The points of continuity are the points where a function exist and has some…

Q: Find the values of a and b that make f continuous everywhere. x2 – 4 - if x 3 a = b =

A: Given that,

Q: is the function f(x) = 1/(x-2) continuous on [1,3]? Justify your answer.

A:

Q: Find the values of a and b that make f continuous everywhere. f(x) =    (x2 − 4)/x-2        if x < 2…

A: Given fx= x2-4x-2 if x&lt;2ax2-bx+1   if 2≤x&lt;34x-a+b      if x≥3Here f is continuous everywhere…

Q: Answer true or false. If f is not piecewise continuous on  [0, ∞>),  then  ℒ{f(t)}  will not exist.

A: Given problem:- If f is not piecewise continuous on [0, ∞),then ℒ{f(t)} will not exist.  True…

Q: Define f(x) = (x2 - 81)/(x - 9) at x = 9 so that the function becomes continuous at 9.

A: Concept: A definition of a function is that a relation from a set of inputs to a set of possible…

Q: Define f(x) =(x2 - 81)/(x - 9)at x = 9 so that the function becomes continuous at 9.

A: Given function is fx=x2-81x-9. To define function fxso that the function becomes continuous at x=9.…

Q: Find the values of a and b that make f continuous everywhere. 2-4 x 2 if x < 2 f(x) if 2 s x< 3 if x…

A: To determine the values of a and b so that f(x) is continuous everywhere.

Q: nuous

A: The function f is continuous at some point c of its domain if the limit of f(x), as x approaches c…

Q: Write a delta - epsilon proof that shows that the function f(x) = 3x – 5 is continuous at æ = 2

A: Let ε&gt;0 be given. Also let 0&lt;δ&lt;min1,ε3. Then for x-2&lt;δ,…

Q: Define 1 if x 2 Determine the values of a and b such that f(x) is continuous for all x.

A:

Q: Determine whether a function is continuous at a given number. If it is discontinuous, identify which…

A: Given function f(x) = -2x +3  for x≤1   and f(x) = x2  for  x &gt; 1

Q: Let 4 – x² if x > 1 f(r) if x < 1 Determine whether or not f (x) is continuous at r = 1.

A: If left hand limit and right hand limit same, then f(x) is continuous at x=1.

Q: Give an example of functions f and g such that f (g(x)) is continuous but g has at least one…

A:

Q: In The given question, , determine whether the statement is true or false. If it is false, explain…

A: we have to tell whether the given statement is true or false. Statement : If a function is…

Q: Let f : X → Y be a continuous function. If X is disconnected then so is f(X). True False

A: Let f : X → Y be a continuous function. If X is disconnected then so is f(X).

Q: { -2x + 3 x 1

A: We have given a piecewise define a function fx which definition change at x=1. The functions…

Q: ずx 1

A:

Q: Let ƒ be the function given by ƒ(x) = (x-2)²(x+3). For what values of x is f not continuous?

A: The given function is fx=(x-2)2·(x+3)(x-2)·(x+1) We have to find the values of x, for which f is not…

Q: Let f : X 'n Y be a continuous function. If X is disconnected then so is f(X). True False

A: As image of a connected set is connected in of every continuous function.

Q: Find the values of a and b that make f continuous everywhere. x² - 4 if x < 2 f(x) = x-2 ax² if 2 ≤…

A:

Q: Provide an example of function f: R → R which is continuous at exactly one point and discontinuous…

A:

Q: Suppose that f is a continuous function such that | f(x) dz = -12. Find (*") dr.

A:

Q: Find the values of a and b that make f continuous everywhere. x2 - 4 if x 3

A: Given function is,

Q: Determine whether the following function is continuous at a. f(x) = /x- 7; a = 1

A: Topic :- Continuity

Q: Find the values of a and b that make f continuous everywhere. x² – - 4 if x < 2 X - 2 f(x) ax2 - bx…

A: Please refer the attached image for complete solution.

Q: Determine the domain of the function and prove that it is continuous on its domain f(x) = √(x2+9)

A: Solution:Given     f(x)=x2+9To find the domain of the function  and to prove f is continous on its…

Q: suppose that f is a function satisfy |f(x)|&lt;=|x| for all x. Show that f is continuous at f = 0.…

A: Suppose that there is a function f that satisfies

Q: Suppose fx) is a continuous function. Then a function F(x) Such that F'(x) =f{x) is called:

A: Given:- Suppose f(x) is a continuous function Then a function F(x) F'(x) = f(x) is called

Q: Determine whether the function is continuous at the given points. x+2 if x22 : 2,0 x if x<2 f(x) =…

A:

Q: Determine algebraically if f is continuous at x= 0.

A:

Q: Determine if the given function is continuous at a given value of x. 2. f(x) = x² - 4x – 2 at x = 1…

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

Q: Determine if the given function is continuous at a given value of x.

A: This question is related to limits and continuity, we will solve it using given information.

Q: Use the definition of continuity to determine whether the shown function is continuous at a = 0.

A:

Q: Let f(x) = −2/x and g be the function defined b)Is f . g continuous at x = 3? If not, does…

A: limit of the composite function

Q: and if the function is differentiable at x

A: The Given function is f(x)=x+33  ,  a=-3

Q: Recall from calculus, if a function is differentiable at a point c, then it is continuous at c, but…

A:

Q: Suppose that the function f(x) = {x“ + 1, x>-1 x <-1 is continuous on R, then a = lax, %3D 1 2 No…

A: The function is given by fx = x2+1, x≥-1ax, x&lt;-1 To evaluate: The value of a if the function is…

Q: Determine whether the function is continuous at the given points. x+30 if x26 6, 0 if x <6 f(x) = Is…

A: Solution

Q: Decide if the following function is continuous using limits. x1.

A: Given,          gx=2xx&lt;13x=13x2+3x&gt;1

Q: Find the values of a and b that make f continuous everywhere: x²-4 if x 3 -

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

Q: The graph of the function f'(x) of a continuous function f is shown. On what intervals is f concave…

A: It is given that,the graph of the function f'(x) of a continuous function f.  We have to find…

Q: Prove if f and g are both functions that are continuous at some point a, then the difference f - g…

A:

Q: f(x) = X-5 if xŹ 2 at x = 2 2x if x< 2

A:

Q: Find the values of a and b that make f continuous everywhere x2 4 - if x 3 a %3D b =

A:

Q: Determine whether the statement is true or false. If f(x) is continuous at x = c, then so is f(x).…

A: Solution is given as below:

Q: Find the numbers at which f is discontinuous. At which of these numbers is f continuous form right,…

A:

Q: x 2

A: Consider the function f(x)=x-1              ,       x≤02x2-3x+1    ,       0&lt;x≤23x3-x2          ,…

Q: h(x) = x+1 %3D at x = 1 x2-1

A: Function f(x) is continuous at a point x=a :Function should be defined at x=a, and  limx→a-f(x) =…

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.