Limit Laws

Addition Law

\displaystyle \boxed{\lim_{x\to c}(f(x)+g(x))=\lim_{x\to c}f(x)+\lim_{x\to c}g(x)}
provided both \lim_{x\to c}f(x) and \lim_{x\to c}g(x) exist.

Subtraction Law

\displaystyle \boxed{\lim_{x\to c}(f(x)-g(x))=\lim_{x\to c}f(x)-\lim_{x\to c}g(x)}
provided both \lim_{x\to c}f(x) and \lim_{x\to c}g(x) exist.

Multiplication Law

\displaystyle \boxed{\lim_{x\to c}(f(x)\cdot g(x))=\lim_{x\to c}f(x)\cdot\lim_{x\to c}g(x)}
provided both \lim_{x\to c}f(x) and \lim_{x\to c}g(x) exist.

Division Law

\displaystyle \boxed{\lim_{x\to c}\frac{f(x)}{g(x)}=\frac{\lim_{x\to c}f(x)}{\lim_{x\to c}g(x)}}
provided both limits on the right exist, and \lim_{x\to c}g(x)\neq 0.

Logarithm Technique

If \displaystyle \lim_{x\to c}\ln f(x)=a, then \displaystyle \lim_{x\to c}f(x)=e^a.

Advertisements

About mathtuition88

http://mathtuition88.com
This entry was posted in math and tagged . Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s