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0

$begingroup$

Let $f(x,y)$ and $g(x)$ be functions such that

1. 
   $lim_{xrightarrow x_0} g(x) = G$.


2. 
   $g(x) ne G$ for all values of $x$ in a punctured neighborhood of $x=x_0$.


3. 
   $f(x,y)$ is continuous at all points where $xne x_0$.

Are these sufficient conditions to assert the following equality?

$$lim_{x rightarrow x_0} f(x,g(x)) = lim_{x rightarrow x_0} f(x,G)$$

If not, what would be sufficient conditions?

limits

share|cite|improve this question

asked Mar 10 at 3:26

Trevor KafkaTrevor Kafka

5308

$endgroup$

add a comment | 

0

$begingroup$

Let $f(x,y)$ and $g(x)$ be functions such that

1. 
   $lim_{xrightarrow x_0} g(x) = G$.


2. 
   $g(x) ne G$ for all values of $x$ in a punctured neighborhood of $x=x_0$.


3. 
   $f(x,y)$ is continuous at all points where $xne x_0$.

Are these sufficient conditions to assert the following equality?

$$lim_{x rightarrow x_0} f(x,g(x)) = lim_{x rightarrow x_0} f(x,G)$$

If not, what would be sufficient conditions?

limits

share|cite|improve this question

asked Mar 10 at 3:26

Trevor KafkaTrevor Kafka

5308

$endgroup$

add a comment | 

$begingroup$

Let $f(x,y)$ and $g(x)$ be functions such that

1. 
   $lim_{xrightarrow x_0} g(x) = G$.


2. 
   $g(x) ne G$ for all values of $x$ in a punctured neighborhood of $x=x_0$.


3. 
   $f(x,y)$ is continuous at all points where $xne x_0$.

Are these sufficient conditions to assert the following equality?

$$lim_{x rightarrow x_0} f(x,g(x)) = lim_{x rightarrow x_0} f(x,G)$$

If not, what would be sufficient conditions?

limits

share|cite|improve this question

asked Mar 10 at 3:26

Trevor KafkaTrevor Kafka

5308

$endgroup$

share|cite|improve this question

asked Mar 10 at 3:26

Trevor KafkaTrevor Kafka

5308

share|cite|improve this question

asked Mar 10 at 3:26

Trevor KafkaTrevor Kafka

5308

asked Mar 10 at 3:26

Trevor KafkaTrevor Kafka

5308

asked Mar 10 at 3:26

Trevor KafkaTrevor Kafka

5308