L 39;hopital 39;s Rule For Indeterminate Forms Homework

The following problems involve the use of l'Hopital's Rule. It is used to circumvent the common indeterminate forms $ \frac "0" 0 $ and $ \frac"\infty" \infty $ when computing limits. There are numerous forms of l"Hopital's Rule, whose verifications require advanced techniques in calculus, but which can be found in many calculus books. This link will show you the plausibility of l'Hopital's Rule. Following are two of the forms of l'Hopital's Rule.

l 39;hopital 39;s rule for indeterminate forms homework

In both forms of l'Hopital's Rule it should be noted that you are required to differentiate (separately) the numerator and denominator of the ratio if either of the indeterminate forms $ \frac "0" 0 $ or $ \frac"\infty" \infty $ arises in the computation of a limit. Do not confuse l'Hopital's Rule with the Quotient Rule for derivatives. Here is a simple illustration of Theorem 1.EXAMPLE 1: $$ \displaystyle \lim_x \rightarrow 2 \fracx-2x^2-4 = \frac" 2-2" (2)^2-4 = \frac "0" 0 $$(Now apply Theorem 1. Differentiate top and bottom separately.)$$ = \displaystyle \lim_x \rightarrow 2 \frac1-02x-0 $$$$ = \displaystyle \lim_x \rightarrow 2 \frac12x $$$$ = \frac12(2) $$ $$ = \frac14 $$ Here is a simple illustration of Theorem 1. 350c69d7ab