### Home > APCALC > Chapter 12 > Lesson 12.2.2 > Problem12-85

12-85.

Multiple Choice: Which of the following limits equals $\cos(2)$?

1. $\lim\limits _ { x \rightarrow 0 } \frac { \operatorname { sin } ( x + 2 ) - \operatorname { sin } ( 2 ) } { x }$

1. $\lim\limits _ { x \rightarrow 0 } \frac { \operatorname { sin } ( 2 + x ) - \operatorname { sin } ( 2 - x ) } { 2 x }$

1. $\lim\limits _ { x \rightarrow 2 } \frac { \operatorname { sin } ( x ) - \operatorname { sin } ( 2 ) } { x - 2 }$

1. I

1. III

1. I, III

1. I, II, III

1. I, II

These are all forms of the derivative of $\sin(x)$ at $x = 2$.
What is the derivative of $\sin(x)$?