Answer to Question #305244 in Calculus for Xvii

Question

Evaluate through constructing table of values

Lim In x 1-cos t/sint

t→0

Answer 1

Solution

For the given limit

$\lim_{t\rightarrow 0}\frac{1-cost}{sint}$

For the function $f(t)=\frac{1-cos(t)}{sin(t)}$

The table of values when $t\rightarrow 0$ (t approaches zero) is

We can see from the table,

$\lim_{t\rightarrow 0}\frac{1-cost}{sint}=0$