True or False? In Exercises 87–92, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If f ( x ) = g ( x ) + c , then f ′ ( x ) = g ′ ( x ) .
True or False? In Exercises 87–92, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If f ( x ) = g ( x ) + c , then f ′ ( x ) = g ′ ( x ) .
Solution Summary: The author analyzes whether the statement, "if f(x)=g left[x]right]+c is true or false. The derivative of a constant is zero.
True or False? In Exercises 87–92, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.
If
f
(
x
)
=
g
(
x
)
+
c
,
then
f
′
(
x
)
=
g
′
(
x
)
.
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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