Question

It is known that limx→0sin(2x)2x=1.
what is limx→0tan(2x)6xsec(3x)?

Answer 1

To find the limit limx→0tan(2x)/6xsec(3x), we can use the given limit limx→0sin(2x)/2x=1. First, let's simplify the expression by dividing both the numerator and denominator by 2x. This gives us tan(2x)/(6xsec(3x)) = (tan(2x)/2x)/(6sec(3x)). Now, as x approaches 0, the term tan(2x)/2x approaches 1 (as given), and sec(3x) approaches 1. Therefore, the limit of the expression is 1/6.

Step-by-step explanation:

To find the limit <em>lim</em>x→0&nbsp;tan(2x)/6xsec(3x), we can use the given limit <em>lim</em>x→0&nbsp;sin(2x)/2x=1.&nbsp;First, let's simplify the expression by dividing both the numerator and denominator by 2x. This gives us tan(2x)/(6xsec(3x)) = (tan(2x)/2x)/(6sec(3x)). Now, as x approaches 0, the term tan(2x)/2x approaches 1 (as given), and sec(3x) approaches 1. Therefore, the limit of the expression is 1/6.