Taxiing Speed A study of a new keyboard layout for smartphones found that the average number of words users could text per minute could be approximated by N ( t ) = 32 ( t + 2 ) t + 5 Where t is the number of days of practice with the keyboard. What was the average number of words users could text with the new layout at the beginning of the study? What was the average number of words users could text after using the layout for 1 week? Find and interpret the horizontal asymptote of N .
Taxiing Speed A study of a new keyboard layout for smartphones found that the average number of words users could text per minute could be approximated by N ( t ) = 32 ( t + 2 ) t + 5 Where t is the number of days of practice with the keyboard. What was the average number of words users could text with the new layout at the beginning of the study? What was the average number of words users could text after using the layout for 1 week? Find and interpret the horizontal asymptote of N .
Taxiing Speed A study of a new keyboard layout for smartphones found that the average number of words users could text per minute could be approximated by
N
(
t
)
=
32
(
t
+
2
)
t
+
5
Where
t
is the number of days of practice with the keyboard.
What was the average number of words users could text with the new layout at the beginning of the study?
What was the average number of words users could text after using the layout for
1
week?
Find and interpret the horizontal asymptote of
N
.
3.
Consider the sequences of functions fn: [-T, π] → R,
sin(n²x)
n(2)
n
(i) Find a function f : [-T, π] R such that fnf pointwise as
n∞. Further, show that f uniformly on [-T,π] as n→ ∞.
[20 Marks]
(ii) Does the sequence of derivatives f(x) has a pointwise limit on [-7,π]?
Justify your answer.
[10 Marks]
Good Day,
Please assist with the following.
Regards,
For each given function f(x) find f'(x) using the rules learned in section 9.5.
1. f(x)=x32
32x
2. f(x)=7x+13
3. f(x) =
x4
4. f(x) = √√x³
5. f(x) = 3x²+
3
x2
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