Question

Use continuity to evaluate the limit. lim x→ 2 sin(x sin(x))

Answer 1

The limit of the function sin(x sin(x)) as x approaches 2 is found by directly substituting 2 into the function due to the continuity of the sine function.

Step-by-step explanation:

To evaluate the limit of the function sin(x sin(x)) as x approaches 2, we can use the continuity property of the sine function. The sine function is continuous everywhere, which means we can simply substitute the value x = 2 directly into the function to find the limit.

The calculation is as follows:

lim x → 2 sin(x sin(x)) = sin(2 sin(2))

Now, we calculate the sine of 2 which is a known value and then take the sine of the resulting number:

sin(2)is a known value that can be found using a calculator or trigonometric tables. After finding this value, we simply take the sine of it to get our final answer.