Linear approximation example: the table gives the population of Nepal (in ... Use
a linear approximation to approximate the population in June of 1989. 1989 is ...
Linear approximation example: the table gives the population R Ð>Ñ of Nepal (in millions) in June of each year: > R Ð>Ñ
"*)& "(Þ!%
"**! "*Þ$$
"**& #"Þ*"
#!!! #%Þ(!
#!!& #(Þ')
Use a linear approximation to approximate the population in June of 1989.
1989 is close to 1990 (a time when we have some actual data), so we look at the linear approximation ( œ tangent line approximation) to the graph of R Ð>Ñ at + œ "**!Þ PÐ>Ñ
œ R Ð"**!Ñ R w Ð"**!ÑÐ> "**!Ñ œ "*Þ$$ R w Ð"**!ÑÐ> "**!Ñ
We need to estimate R w Ð"**!Ñ À we do that, in the usual way, by averaging the slope of two secant lines: "*Þ$$ "*Þ$$ "(Þ!% R w Ð"**!Ñ ¸ "# Ð #"Þ*" "**& "**! Ñ Ð "**! "*)& ÑÑ ¸
¸ "# Ð!Þ&"'! !Þ%&)!Ñ œ !Þ%)(! Ðmillions/year) So
The graph below shows the population curve and also the tangent line approximation.
Example using differentials: The radius of a circular disk is given as 24 cm with a maximum error in measurement of 0.2 cm. Use differentials to estimate the maximum error in the calculated area of the disk. E œ 1
