Evaluate through constructing table of values
Lim In x 1-cos t/sint
t→0
Solution
For the given limit
limt→01−costsint\lim_{t\rightarrow 0}\frac{1-cost}{sint}limt→0sint1−cost
For the function f(t)=1−cos(t)sin(t)f(t)=\frac{1-cos(t)}{sin(t)}f(t)=sin(t)1−cos(t)
The table of values when t→0t\rightarrow 0t→0 (t approaches zero) is
We can see from the table,
limt→01−costsint=0\lim_{t\rightarrow 0}\frac{1-cost}{sint}=0limt→0sint1−cost=0
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