Question

Evaluate the following limit:
lim (as x approaches 0) sin(2x)/2.

Answer 1

The limit as x approaches 0 of sin(2x)/2 is evaluated by rewriting the expression to fit the standard trigonometric limit, ending with a final value of 1/2.

Step-by-step explanation:

The limit in question is lim (as x approaches 0) sin(2x)/2. To evaluate this limit, we can use the standard trigonometric limit that states lim (as x approaches 0) sin(x)/x = 1. Applying this knowledge, we can manipulate the given expression to fit this form:

• sin(2x)/2 can be rewritten as (1/2) · sin(2x)/2x when we multiply and divide by 2.
• The limit of this expression as x approaches 0 is (1/2) · lim (as x approaches 0) sin(2x)/2x.
• Using the standard limit, we know that lim (as x approaches 0) sin(2x)/2x = 1.
• Therefore, the final answer is (1/2) · 1 = 1/2.

The evaluated limit as x approaches 0 for sin(2x)/2 is 1/2.