Question

Fill in the blanks for this question.

. lim(x → [infinity])(tan^(-1), sin(1)/1, 1/sqrt(1)) = ____?

Answer 1

The limit of the given expression as x approaches infinity is 0.

Step-by-step explanation:

The given question is asking us to find the limit of the expression lim(x → ∞) tan^(-1)(sin(1)/1) / (1/sqrt(1)) as x approaches infinity.

We can simplify the expression by applying the limit properties. First, we simplify the numerator: tan^(-1)(sin(1)/1) is equal to the angle whose tangent is sin(1)/1. Since sin(1) is a small angle, it approaches 0, and the tangent of 0 is 0. Therefore, the numerator simplifies to 0. The denominator, 1/sqrt(1), simplifies to 1.

So, we have 0/1, which is equal to 0. Therefore, the limit of the given expression as x approaches infinity is 0.