### Home > APCALC > Chapter 10 > Lesson 10.1.4 > Problem10-48

10-48.

Without your calculator, determine the following limits.

1. $\lim\limits _ { x \rightarrow 2 } \frac { 4 ( x - 2 ) ^ { 3 } } { 3 x - 6 }$

Factor the denominator then simplify.

1. $\lim\limits _ { x \rightarrow - \infty } \frac { 4 ( x - 2 ) ^ { 3 } } { 3 x - 6 }$

Since this is a limit at $–∞$, look at the dominant terms.

1. $\lim\limits _ { x \rightarrow 0 } \frac { x \operatorname { sin } ( x ) } { \operatorname { ln } ( x + 1 ) }$

Use l'Hôpital's Rule.

1. $\lim\limits _ { h \rightarrow 0 } \frac { \operatorname { ln } ( x - h ) - \operatorname { ln } ( x ) } { h }$

This is the definition of derivative for $-\ln(x)$.