1.3 The Limit of a Function
fax. Toss bull in air w/ initial velocity 4.8 mly and
initial hight 1.5
M
>(+) = 1.5 + 9.84 - 4.94?
Average Velocity on [t,, t₂]:
tz
Aug. Velocity from (3.4] 5(4)-5(3)
sita (4)
+₂-t
= -24.5 m/s
Intervals [3,4] [[3.5,4)] [344] (391,4] [3.449,4]
Any V(~s 1-24.5 -26.95 -28.4
-29.351 -29.39 51
weight of, ball
uffer + seconds
The instantinous velocity is de ned to be the "limiting value"
of the avy. Velocity, us
+(x) =
"the width
Joes
to
O. We can
"guess" that the instantaneous velocity at t=4 seconds
7 -29.479
JxF6 -? What is the domain?
X-3
メキア
**3. (-6,3) U(3,∞) How do values of X behave us
*≥-6
Intuitive Det. of a Limit:
Suppose f is retired on
an open interval containing
u, except possibly
a. If
* approuches ??
☑
fox) (uppet.) Note: 0.15 = t
25 0.16905
2.9 0.16213
2.44 0.166671
2.99
we can make fox) unbitrarily ↑ 301/0.16662
close to some numbe by
3.1/0.16621
8.79
taking x suf ciently close to
ay then m fox) = L
3.5/0.16441
As x
approaches 3 it
fas is approaching to
append
is that fi fi fi
fax. Toss bull in air w/ initial velocity 4.8 mly and
initial hight 1.5
M
>(+) = 1.5 + 9.84 - 4.94?
Average Velocity on [t,, t₂]:
tz
Aug. Velocity from (3.4] 5(4)-5(3)
sita (4)
+₂-t
= -24.5 m/s
Intervals [3,4] [[3.5,4)] [344] (391,4] [3.449,4]
Any V(~s 1-24.5 -26.95 -28.4
-29.351 -29.39 51
weight of, ball
uffer + seconds
The instantinous velocity is de ned to be the "limiting value"
of the avy. Velocity, us
+(x) =
"the width
Joes
to
O. We can
"guess" that the instantaneous velocity at t=4 seconds
7 -29.479
JxF6 -? What is the domain?
X-3
メキア
**3. (-6,3) U(3,∞) How do values of X behave us
*≥-6
Intuitive Det. of a Limit:
Suppose f is retired on
an open interval containing
u, except possibly
a. If
* approuches ??
☑
fox) (uppet.) Note: 0.15 = t
25 0.16905
2.9 0.16213
2.44 0.166671
2.99
we can make fox) unbitrarily ↑ 301/0.16662
close to some numbe by
3.1/0.16621
8.79
taking x suf ciently close to
ay then m fox) = L
3.5/0.16441
As x
approaches 3 it
fas is approaching to
append
is that fi fi fi
