Question

Lim x-> infinity of arctan(lnx)

Answer 1

The limit of arctan(lnx) as x approaches infinity is π/2.

Step-by-step explanation:

The limit in question involves a composition of two functions: the natural logarithm (ln) and the arctangent (arctan).

The given limit is:
limx->∞ arctan(lnx)

We can start by evaluating the limit of ln(x) as x approaches infinity. Since the natural logarithm is an increasing function, ln(x) will approach infinity as x approaches infinity.

As x approaches infinity, the value of ln(x) will become very large. This means that arctan(ln(x)) will approach the angle for which tan is infinity, which is π/2 or 90 degrees. Therefore, the limit of arctan(lnx) as x approaches infinity is π/2.

Answer 2

Lim x-> infinity of arctan(lnx)= arctan (infinity), because lnx-----> infinity when x ----> infinity

but arctan (infinity) = Pi/2, so Lim x-> infinity of arctan(lnx)= Pi/2