Review Topics
Limits
The trigonometric functions sine and cosine have four important limit properties:
|
You can use these properties to evaluate many limit problems involving the six basic trigonometric functions.
Example 1: Evaluate
.
Substituting 0 for
x, you find that cos
x approaches 1 and sin
x − 3 approaches −3; hence,
|
Example 2: Evaluate
Because cot
x = cos
x/sin
x, you find
The numerator approaches 1 and the denominator approaches 0 through positive values because we are approaching 0 in the first quadrant; hence, the function increases without bound and
and the function has a vertical asymptote at
x = 0.
Example 3: Evaluate
Multiplying the numerator and the denominator by 4 produces
|
Example 4: Evaluate
.
Because sec
x = 1/cos
x, you find that
|
