Mixing
C an we conclude that $lim_{xto0+}(f*g)(x)= lim_{xto0+}f(x)* lim_{xto0+}g(x)?$
0
$begingroup$
Let $f,g:(0,1)to(0,1)$ be two continuous functions such that $lim_{xto0+}f(x)$ and $lim_{xto0+}g(x)$ exists. If $*:[0,1]times[0,1]to[0,1]$ be continuous then can we conclude that $lim_{xto0+}(f(x)*g(x))= lim_{xto0+}f(x)* lim_{xto0+}g(x)?$
I think that will be true but I couldn’t conclude this using proper logic.
Please help me.
continuity
asked Jan 17 at 14:39
JaveJave
472114
$endgroup$
|
show 2 more comments
0
$begingroup$
Let $f,g:(0,1)to(0,1)$ be two continuous functions such that $lim_{xto0+}f(x)$ and $lim_{xto0+}g(x)$ exists. If $*:[0,1]times[0,1]to[0,1]$ be continuous then can we conclude that $lim_{xto0+}(f(x)*g(x))= lim_{xto0+}f(x)* lim_{xto0+}g(x)?$
I think that will be true but I couldn’t conclude this using proper logic.
Please help me.
continuity
asked Jan 17 at 14:39
JaveJave
472114
$endgroup$
$begingroup$
The notation doesn't make sense. If $*$ is a function defined on $[0,1]$, what is $f*g$ supposed to be?
$endgroup$
– Git Gud
Jan 17 at 14:42
$begingroup$
Modified it properly
$endgroup$
– Jave
Jan 17 at 14:43
$begingroup$
Still not clear. On the LHS is the function $xmapsto *left(g(x)right)cdot f(x)$? Or perhaps you mean that $*$ is a function from $[0,1]^2$ to $[0,1]$ and you're using infix notation.
$endgroup$
– Git Gud
Jan 17 at 14:46
$begingroup$
Yes yes I am sorry
$endgroup$
– Jave
Jan 17 at 14:48
$begingroup$
Do you know multivariable calculus? Can you prove that $xmapsto (f(x), g(x))$ is continuous? Do you know that the composition of continuous functions is continuous?
$endgroup$
– Git Gud
Jan 17 at 14:57
|
show 2 more comments
0
0
0
$begingroup$
Let $f,g:(0,1)to(0,1)$ be two continuous functions such that $lim_{xto0+}f(x)$ and $lim_{xto0+}g(x)$ exists. If $*:[0,1]times[0,1]to[0,1]$ be continuous then can we conclude that $lim_{xto0+}(f(x)*g(x))= lim_{xto0+}f(x)* lim_{xto0+}g(x)?$
I think that will be true but I couldn’t conclude this using proper logic.
Please help me.
continuity
asked Jan 17 at 14:39
JaveJave
472114
$endgroup$
Let $f,g:(0,1)to(0,1)$ be two continuous functions such that $lim_{xto0+}f(x)$ and $lim_{xto0+}g(x)$ exists. If $*:[0,1]times[0,1]to[0,1]$ be continuous then can we conclude that $lim_{xto0+}(f(x)*g(x))= lim_{xto0+}f(x)* lim_{xto0+}g(x)?$
I think that will be true but I couldn’t conclude this using proper logic.
Please help me.
continuity
continuity
asked Jan 17 at 14:39
JaveJave
472114
asked Jan 17 at 14:39
JaveJave
472114
edited Jan 17 at 14:48
Jave
asked Jan 17 at 14:39
JaveJave
472114
asked Jan 17 at 14:39
JaveJave
472114
asked Jan 17 at 14:39
JaveJave
472114
472114
$begingroup$
The notation doesn't make sense. If $*$ is a function defined on $[0,1]$, what is $f*g$ supposed to be?
$endgroup$
– Git Gud
Jan 17 at 14:42
$begingroup$
Modified it properly
$endgroup$
– Jave
Jan 17 at 14:43
$begingroup$
Still not clear. On the LHS is the function $xmapsto *left(g(x)right)cdot f(x)$? Or perhaps you mean that $*$ is a function from $[0,1]^2$ to $[0,1]$ and you're using infix notation.
$endgroup$
– Git Gud
Jan 17 at 14:46
$begingroup$
Yes yes I am sorry
$endgroup$
– Jave
Jan 17 at 14:48
$begingroup$
Do you know multivariable calculus? Can you prove that $xmapsto (f(x), g(x))$ is continuous? Do you know that the composition of continuous functions is continuous?
$endgroup$
– Git Gud
Jan 17 at 14:57
|
show 2 more comments
$begingroup$
The notation doesn't make sense. If $*$ is a function defined on $[0,1]$, what is $f*g$ supposed to be?
$endgroup$
– Git Gud
Jan 17 at 14:42
$begingroup$
Modified it properly
$endgroup$
– Jave
Jan 17 at 14:43
$begingroup$
Still not clear. On the LHS is the function $xmapsto *left(g(x)right)cdot f(x)$? Or perhaps you mean that $*$ is a function from $[0,1]^2$ to $[0,1]$ and you're using infix notation.
$endgroup$
– Git Gud
Jan 17 at 14:46
$begingroup$
Yes yes I am sorry
$endgroup$
– Jave
Jan 17 at 14:48
$begingroup$
Do you know multivariable calculus? Can you prove that $xmapsto (f(x), g(x))$ is continuous? Do you know that the composition of continuous functions is continuous?
$endgroup$
– Git Gud
Jan 17 at 14:57
$begingroup$
The notation doesn't make sense. If $*$ is a function defined on $[0,1]$, what is $f*g$ supposed to be?
$endgroup$
– Git Gud
Jan 17 at 14:42
$begingroup$
The notation doesn't make sense. If $*$ is a function defined on $[0,1]$, what is $f*g$ supposed to be?
$endgroup$
– Git Gud
Jan 17 at 14:42
$begingroup$
Modified it properly
$endgroup$
– Jave
Jan 17 at 14:43
$begingroup$
Modified it properly
$endgroup$
– Jave
Jan 17 at 14:43
$begingroup$
Still not clear. On the LHS is the function $xmapsto *left(g(x)right)cdot f(x)$? Or perhaps you mean that $*$ is a function from $[0,1]^2$ to $[0,1]$ and you're using infix notation.
$endgroup$
– Git Gud
Jan 17 at 14:46
$begingroup$
Still not clear. On the LHS is the function $xmapsto *left(g(x)right)cdot f(x)$? Or perhaps you mean that $*$ is a function from $[0,1]^2$ to $[0,1]$ and you're using infix notation.
$endgroup$
– Git Gud
Jan 17 at 14:46
$begingroup$
Yes yes I am sorry
$endgroup$
– Jave
Jan 17 at 14:48
$begingroup$
Yes yes I am sorry
$endgroup$
– Jave
Jan 17 at 14:48
$begingroup$
Do you know multivariable calculus? Can you prove that $xmapsto (f(x), g(x))$ is continuous? Do you know that the composition of continuous functions is continuous?
$endgroup$
– Git Gud
Jan 17 at 14:57
$begingroup$
Do you know multivariable calculus? Can you prove that $xmapsto (f(x), g(x))$ is continuous? Do you know that the composition of continuous functions is continuous?
$endgroup$
– Git Gud
Jan 17 at 14:57
|
show 2 more comments
0
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$begingroup$
The notation doesn't make sense. If $*$ is a function defined on $[0,1]$, what is $f*g$ supposed to be?
$endgroup$
– Git Gud
Jan 17 at 14:42
$begingroup$
Modified it properly
$endgroup$
– Jave
Jan 17 at 14:43
$begingroup$
Still not clear. On the LHS is the function $xmapsto *left(g(x)right)cdot f(x)$? Or perhaps you mean that $*$ is a function from $[0,1]^2$ to $[0,1]$ and you're using infix notation.
$endgroup$
– Git Gud
Jan 17 at 14:46
$begingroup$
Yes yes I am sorry
$endgroup$
– Jave
Jan 17 at 14:48
$begingroup$
Do you know multivariable calculus? Can you prove that $xmapsto (f(x), g(x))$ is continuous? Do you know that the composition of continuous functions is continuous?
$endgroup$
– Git Gud
Jan 17 at 14:57