Limit of a Function
Problem:
Find the limit
lim
t →0
sin
(
3t
)
sin
(
t
)
Formula: NA
Figure: NA
Solution:
First multiply numerator and denominator by 3t.
lim
t →0
sin
(
3t
)
sin
(
t
)
=lim
t→ 0
sin
(
3t
)
t
Use limit properties and theorems to rewrite the above limit as the product of two limits and a
constant.
¿3 lim
t → 0
sin
(
3t
)
t×lim
t → 0
sin
(
T
)
T=1
The second limit is easily calculated as follows,
lim
t →0
sin
(
3t
)
sin
(
t
)
=3
Quotient Rule
Problem:
Find the derivative of the function:
y=ln x
2x2
Formula: NA
Figure: NA
Solution:
y'=
(
ln x
)
'
(
2x2
)
−
(
ln x
) (
2x
)
'
(
2x2
)
2
