Part C: Check the continuity of the following function at x- 1 (1+x f(x) -x 2-x if x<-1 if-1sx<1 if x21

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: Determine the domain of the function and prove that it is continuous on its domain using the Laws…

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Q: Determine the domain of the function and prove that it is continuous on its domain using Theorems…

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Q: Is it possible to determine f (7) if f (x) = 3 for all x &lt; 7 and f is right-continuous at x = 7?…

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Q: Check the continuity of the following function at x = 1 (1+x f(x) = {x? 2-x if x <-1 if -1sx<1 if x…

A: A function f(x) is continuous at a point x=a if f(a) is well defined and the left hand side and…

Q: 4x f (x)=- x2 +4 %3D

A: f(x)=-4xx2+4

Q: If f(x) = |x − 1| + |x + 3|, then discuss the continuity and differentiability of the function at x…

A: Consider the given function fx=x-1+x+3 First, check the continuity of the function at x=1 Since a…

Q: Consider the following function. x2 - x - 56 f(x) = x2 + 7x Find each value. (If an answer does not…

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Q: Graph the function 1, x <-1 -1 < x < 0 -x, x = 0 f(x) = 1, 0 < x < 1 x 2 1. -x, 1, Then discuss, in…

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Q: Check the continuity of the functions f given below at 1 and 2. x +1 if x < 1 f(x) = { 2x 1+ x'if x…

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Q: Check the continuity of the following function at x = 1 (1+x f(x) = {x? 2-x if x<-1 if -1sx<1 if x…

A: A function is continuous at  x = a if the following condition is satisfied

Q: Show that the function f(x) = x' + 3x² is continuous at every real number a.

A: fx=x3+3x2

Q: Use the definition of continuity to decide if the following function is continuous at a = -1. -1.0x²…

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Q: 3. Analyze the continuity of this function. If there are discontinuities, state the type. [x² + 2x…

A: Given the functionfx=x2+2xx≤14-x1&lt;x&lt;3x-3x≥3we discuss about the discontinuity of the…

Q: Suppose that f(x) = 2 for x &lt; 3 and f(x) = -4 for x &gt; 3. (a) What is f (3) if f is…

A: For x&lt;3,f(x) = 2For x&gt;3,f(x) =-4Part (a) - f(3) = ? when f(x) is left continuous.f(3) =…

Q: Discuss the continuity of the following function: 2* (1- x), x0 x < 0 x = 0

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Q: Let f(x)=x3-7x. Calculate the difference quotient [f(3+h)-f(3)]/h for  h=0.1 h=0.01 h=-0.01 h=-0.1

A: when h = 0.1,

Q: 0 < x < 1 1 < x < 2 X = 3 3 < x <4 x = 5 2 - x , 3 Test continuity for the following function: F(x)…

A: Given: Fx=2-x,0≤x&lt;13,1≤x&lt;22,x=3-2x-2,3&lt;x≤40,x=5

Q: 3. Analyze the continuity of this function. If there are discontinuities, state the type. [x² + 2x…

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Q: Letf be a function defined below. x² + 3x] if xS0,x = 3 f(x) = || x+ 3 x+1 if T >x>0 x21 if Discuss…

A: The function is not defined at the point x=-3 . Hence the function is not continuous at the point…

Q: Check the continuity and differentiabilty of f (x) = |x − 1| + |x − 2| at x = 2.

A: Given :  The given function is ;  f(x) = x-1 + x-2 To find : We have to check the continuity and…

Q: 3. Analyze the continuity of this function. If there are discontinuities, state the type. [x² + 2x…

A: To check for the continuity of the function fx=x2+2xx≤14-x1&lt;x&lt;3x-3x≥3

Q: Q3) Test the continuity of the function f(x): -15x <0 0S X< 2 F(x) = 2х— 1 x+ 3 X = 2

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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: Let f(x)= 1 Use a 8- e proof to show that f is continuous at x = = 2. X-1

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Q: Q4) Test the continuity of the function f(x): - 2< x < 0 0< X<1 X = 1 F(x) = Зх —2 2x +1 3

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Q: 3. Analyze the continuity of this function. If there are discontinuities, state the type. [x² + 2x…

A: Given the function,fx=x2+2xx≤14-x1&lt;x&lt;3x-3x≥3

Q: 3. Analyze the continuity of this function. If there are discontinuities, state the type. [x² + 2x…

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Q: Define g(-1) in a way that extends g(x) = 1 to be continuous at x= - 1. x² -x-2 2 9(-1)-D

A: Given that: g(x)=x2-1x2-x-2

Q: Determine whether the statement is true or false. If f is continuous at 5 and f(5) = 3 and f(4) = 3,…

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Q: Is it possible to determine f(7) if f(x) = 3 for all x &lt; 7 and f is rightcontinuous at x = 7?…

A: Solution: Consider the given that f(x) = 3 for all x &lt; 7 f is right continuous at x = 7  The…

Q: Letf(x)= 1/x-1 Use a 8-e proof to show that f is continuous at x = 2.

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Q: Discuss the continuity of the following function: (2* (1– x), x 0 x = 0

A: Consider the given:

Q: Q4) Test the continuity of the function f(x): - 2 < x < 0 0< X <1 X = 1 F(x) = 3x - 2 2х + 1 3

A: Fx= 3x-2  -2≤x&lt;02x+1     0≤x&lt;13       x=1 We know that a polynomial function is always…

Q: x' - 27 x² -9 (c) at x = 3 and x = -3

A: First of all to find critical points put the denominator equal to zero. x2 - 9 = 0 x 2 = 9 x = 3, -3…

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

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Q: Determine whether the following function is continuous at a. Use the continuity checklist to justify…

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Q: Suppose that f is a function given by f(x) = -2x + 7. Which is TRUE about the function? O lim/→0…

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Q: (a) A function f(x) is defined by 3x + 4; x 2 1 -5 x+6B f(x) = -5 -3x – 4; Discuss the continuity…

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Q: Test continuity for the following function : x < 0 x + f(x) ={-x3 -1 0 < x < 1 1< x <2 %3D 1 X = 2…

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Q: Graph the function

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

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Q: Part C: Check the continuity of the following function at x 1 1+x if x<-1 if -1sx<1 if x 21 f(x)…

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Q: Test the continuity of the following function at x = 1 (2 — х, х 1 2

A: Given data: The expression for the given function is f(x)=2-x, x&lt;11,        x=13x2,    x&gt;1…

Q: (b). Analyze general properties of continuity and discuss the continuity of the following. (1). f(x)…

A: Discuss the continuity of the functions.       i) fx=x2-93        iii) fx=xx+1x-2

Q: Check the continuity of the following function at x = 1 (1+x f(x) =x (2-x if x <-1 if -1sx<1 if x21

A: Check for left hand limit and right hand limit and check whether they are equal or not.

Q: Q12: Discuss the continuity of function f(x) at x-3 x²-9 if x # 3 6 if x = 3 F(x) = {x-3 %3D

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Q: Let f(x) = 2x² + 5x - 7 x-1 = 1 and determine what value for f(1) would make Show that f(x) has a…

A: Solution of given question is written in below steps.

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.