Is my answer to this lim question correct?

[38175425]

The question:

Translation:
若lim x➝3 f(x)存在
if lim x➝3 f(x) exists
My work:

 

[Harry_the_cat]

So what is "a"?

 

[nasi112]

\(\displaystyle \lim_{x\rightarrow 3^{-}} x^2 + 3 = \lim_{x\rightarrow 3^{+}} 2x + a\)

Continue.

 

[Otis]

Is my answer to this … correct?

Hello 38175425. Your work is good, but you're not done. So far, you've answered:

f(3) = ?

We're told the limit at 3 exists; therefore, function f must be continuous at x=3.

If you're still stuck, then sketch a rough graph of f(x) from x=0 to x=5, using the incorrect value a=12, and see what goes wrong at x=3.


[imath]\;[/imath]

 

[Steven G]

Hello 38175425. Your work is good, but you're not done. So far, you've answered:

f(3) = ?

We're told the limit at 3 exists; therefore, function f must be continuous at x=3.

If you're still stuck, then sketch a rough graph of f(x) from x=0 to x=5, using the incorrect value a=12, and see what goes wrong at x=3.


[imath]\;[/imath]

Darn, and I thought that a=12 was correct!