At what point does both right hand and left hand limits exist, but the limit does not exist? Give your...
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Question 1
Consider the function defined by
$$f(x) =
begin{cases}
x^2 - 1, & text{if $x leq 0$}\
x - 2, & text{if $0 < x < 1$}\
c, & text{if $x = 1$}\
-x, & text{if $x > 1$}
end{cases}
$$
(a) At what point does both right hand and left hand limits exist, but the limit does not exist? Give your reason.
(4 marks)
(b) Find the value of $c$ for which $f(x)$ is continuous at $x=1$. Give your reason.
(6 marks)
Current ANSWER:
enter image description here
not sure if answer a is correct.
not sure about the method to solve question b
functions
asked Dec 8 '18 at 11:01
auxy12auxy12
257
$endgroup$
add a comment |
$begingroup$
Question 1
Consider the function defined by
$$f(x) =
begin{cases}
x^2 - 1, & text{if $x leq 0$}\
x - 2, & text{if $0 < x < 1$}\
c, & text{if $x = 1$}\
-x, & text{if $x > 1$}
end{cases}
$$
(a) At what point does both right hand and left hand limits exist, but the limit does not exist? Give your reason.
(4 marks)
(b) Find the value of $c$ for which $f(x)$ is continuous at $x=1$. Give your reason.
(6 marks)
Current ANSWER:
enter image description here
not sure if answer a is correct.
not sure about the method to solve question b
functions
asked Dec 8 '18 at 11:01
auxy12auxy12
257
$endgroup$
$begingroup$
Welcome to MathSE. When you pose a question on this site, it is expected that you include your own thoughts on the problem. Please edit the question to tell us what you know, show what you have attempted, and explain where you are stuck so that you receive answers that address the specific difficulties you are encountering. This tutorial explains how to typeset mathematics on this site.
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– N. F. Taussig
Dec 8 '18 at 11:16
1
$begingroup$
Also, I do not understand how the title relates to the question. Please revise your title.
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– N. F. Taussig
Dec 8 '18 at 11:23
$begingroup$
Your working for part (a) seems very clear. What in particular is your reason for doubt?
$endgroup$
– David K
Dec 8 '18 at 14:15
add a comment |
$begingroup$
Question 1
Consider the function defined by
$$f(x) =
begin{cases}
x^2 - 1, & text{if $x leq 0$}\
x - 2, & text{if $0 < x < 1$}\
c, & text{if $x = 1$}\
-x, & text{if $x > 1$}
end{cases}
$$
(a) At what point does both right hand and left hand limits exist, but the limit does not exist? Give your reason.
(4 marks)
(b) Find the value of $c$ for which $f(x)$ is continuous at $x=1$. Give your reason.
(6 marks)
Current ANSWER:
enter image description here
not sure if answer a is correct.
not sure about the method to solve question b
functions
asked Dec 8 '18 at 11:01
auxy12auxy12
257
$endgroup$
Question 1
Consider the function defined by
$$f(x) =
begin{cases}
x^2 - 1, & text{if $x leq 0$}\
x - 2, & text{if $0 < x < 1$}\
c, & text{if $x = 1$}\
-x, & text{if $x > 1$}
end{cases}
$$
(a) At what point does both right hand and left hand limits exist, but the limit does not exist? Give your reason.
(4 marks)
(b) Find the value of $c$ for which $f(x)$ is continuous at $x=1$. Give your reason.
(6 marks)
Current ANSWER:
enter image description here
not sure if answer a is correct.
not sure about the method to solve question b
functions
functions
asked Dec 8 '18 at 11:01
auxy12auxy12
257
asked Dec 8 '18 at 11:01
auxy12auxy12
257
edited Dec 8 '18 at 11:51
auxy12
asked Dec 8 '18 at 11:01
auxy12auxy12
257
asked Dec 8 '18 at 11:01
auxy12auxy12
257
asked Dec 8 '18 at 11:01
auxy12auxy12
257
257
$begingroup$
Welcome to MathSE. When you pose a question on this site, it is expected that you include your own thoughts on the problem. Please edit the question to tell us what you know, show what you have attempted, and explain where you are stuck so that you receive answers that address the specific difficulties you are encountering. This tutorial explains how to typeset mathematics on this site.
$endgroup$
– N. F. Taussig
Dec 8 '18 at 11:16
1
$begingroup$
Also, I do not understand how the title relates to the question. Please revise your title.
$endgroup$
– N. F. Taussig
Dec 8 '18 at 11:23
$begingroup$
Your working for part (a) seems very clear. What in particular is your reason for doubt?
$endgroup$
– David K
Dec 8 '18 at 14:15
add a comment |
$begingroup$
Welcome to MathSE. When you pose a question on this site, it is expected that you include your own thoughts on the problem. Please edit the question to tell us what you know, show what you have attempted, and explain where you are stuck so that you receive answers that address the specific difficulties you are encountering. This tutorial explains how to typeset mathematics on this site.
$endgroup$
– N. F. Taussig
Dec 8 '18 at 11:16
1
$begingroup$
Also, I do not understand how the title relates to the question. Please revise your title.
$endgroup$
– N. F. Taussig
Dec 8 '18 at 11:23
$begingroup$
Your working for part (a) seems very clear. What in particular is your reason for doubt?
$endgroup$
– David K
Dec 8 '18 at 14:15
$begingroup$
Welcome to MathSE. When you pose a question on this site, it is expected that you include your own thoughts on the problem. Please edit the question to tell us what you know, show what you have attempted, and explain where you are stuck so that you receive answers that address the specific difficulties you are encountering. This tutorial explains how to typeset mathematics on this site.
$endgroup$
– N. F. Taussig
Dec 8 '18 at 11:16
$begingroup$
Welcome to MathSE. When you pose a question on this site, it is expected that you include your own thoughts on the problem. Please edit the question to tell us what you know, show what you have attempted, and explain where you are stuck so that you receive answers that address the specific difficulties you are encountering. This tutorial explains how to typeset mathematics on this site.
$endgroup$
– N. F. Taussig
Dec 8 '18 at 11:16
1
1
$begingroup$
Also, I do not understand how the title relates to the question. Please revise your title.
$endgroup$
– N. F. Taussig
Dec 8 '18 at 11:23
$begingroup$
Also, I do not understand how the title relates to the question. Please revise your title.
$endgroup$
– N. F. Taussig
Dec 8 '18 at 11:23
$begingroup$
Your working for part (a) seems very clear. What in particular is your reason for doubt?
$endgroup$
– David K
Dec 8 '18 at 14:15
$begingroup$
Your working for part (a) seems very clear. What in particular is your reason for doubt?
$endgroup$
– David K
Dec 8 '18 at 14:15
add a comment |
1 Answer
1
active
oldest
votes
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b) for continuity at x=1 at first we have to do L.H.L $f(x)$ at 1 = R.H.L $f(x)$ at 1 =$lim$ x tends to 1 $f(x)$ .
Here ,
L.H.L. of $f(x)$ at x=1 = R.H.L. of $f(x)$ at x=1 = -1
So, for continuity c must be -1
Sorry,for this type of writing.I am not too much familiar with this.
answered Dec 8 '18 at 13:37
Supriyo BanerjeeSupriyo Banerjee
1176
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add a comment |
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b) for continuity at x=1 at first we have to do L.H.L $f(x)$ at 1 = R.H.L $f(x)$ at 1 =$lim$ x tends to 1 $f(x)$ .
Here ,
L.H.L. of $f(x)$ at x=1 = R.H.L. of $f(x)$ at x=1 = -1
So, for continuity c must be -1
Sorry,for this type of writing.I am not too much familiar with this.
answered Dec 8 '18 at 13:37
Supriyo BanerjeeSupriyo Banerjee
1176
$endgroup$
add a comment |
$begingroup$
b) for continuity at x=1 at first we have to do L.H.L $f(x)$ at 1 = R.H.L $f(x)$ at 1 =$lim$ x tends to 1 $f(x)$ .
Here ,
L.H.L. of $f(x)$ at x=1 = R.H.L. of $f(x)$ at x=1 = -1
So, for continuity c must be -1
Sorry,for this type of writing.I am not too much familiar with this.
answered Dec 8 '18 at 13:37
Supriyo BanerjeeSupriyo Banerjee
1176
$endgroup$
add a comment |
$begingroup$
b) for continuity at x=1 at first we have to do L.H.L $f(x)$ at 1 = R.H.L $f(x)$ at 1 =$lim$ x tends to 1 $f(x)$ .
Here ,
L.H.L. of $f(x)$ at x=1 = R.H.L. of $f(x)$ at x=1 = -1
So, for continuity c must be -1
Sorry,for this type of writing.I am not too much familiar with this.
answered Dec 8 '18 at 13:37
Supriyo BanerjeeSupriyo Banerjee
1176
$endgroup$
b) for continuity at x=1 at first we have to do L.H.L $f(x)$ at 1 = R.H.L $f(x)$ at 1 =$lim$ x tends to 1 $f(x)$ .
Here ,
L.H.L. of $f(x)$ at x=1 = R.H.L. of $f(x)$ at x=1 = -1
So, for continuity c must be -1
Sorry,for this type of writing.I am not too much familiar with this.
answered Dec 8 '18 at 13:37
Supriyo BanerjeeSupriyo Banerjee
1176
answered Dec 8 '18 at 13:37
Supriyo BanerjeeSupriyo Banerjee
1176
answered Dec 8 '18 at 13:37
Supriyo BanerjeeSupriyo Banerjee
1176
answered Dec 8 '18 at 13:37
Supriyo BanerjeeSupriyo Banerjee
1176
1176
add a comment |
add a comment |
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$begingroup$
Welcome to MathSE. When you pose a question on this site, it is expected that you include your own thoughts on the problem. Please edit the question to tell us what you know, show what you have attempted, and explain where you are stuck so that you receive answers that address the specific difficulties you are encountering. This tutorial explains how to typeset mathematics on this site.
$endgroup$
– N. F. Taussig
Dec 8 '18 at 11:16
1
$begingroup$
Also, I do not understand how the title relates to the question. Please revise your title.
$endgroup$
– N. F. Taussig
Dec 8 '18 at 11:23
$begingroup$
Your working for part (a) seems very clear. What in particular is your reason for doubt?
$endgroup$
– David K
Dec 8 '18 at 14:15