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Question 9.6
Question 9.6
Solutions
TZ
leumasic
Official
3 months ago
a)
g
′
(
x
)
=
lim
h
→
0
g
(
x
+
h
)
−
g
(
x
)
h
=
lim
h
→
0
f
(
x
+
h
)
+
c
−
(
f
(
x
)
+
c
)
h
=
lim
h
→
0
f
(
x
+
h
)
−
f
(
x
)
h
=
f
′
(
x
)
.
\begin{align*} g'(x)&=\lim_{h\to 0}\frac{g(x+h)-g(x)}{h} \\ &=\lim_{h\to 0}\frac{f(x+h)+c-(f(x)+c)}{h} \\ &=\lim_{h\to 0}\frac{f(x+h)-f(x)}{h} \\ &=f'(x). \end{align*}
g
′
(
x
)
=
h
→
0
lim
h
g
(
x
+
h
)
−
g
(
x
)
=
h
→
0
lim
h
f
(
x
+
h
)
+
c
−
(
f
(
x
)
+
c
)
=
h
→
0
lim
h
f
(
x
+
h
)
−
f
(
x
)
=
f
′
(
x
)
.
b)
g
′
(
x
)
=
lim
h
→
0
g
(
x
+
h
)
−
g
(
x
)
h
=
lim
h
→
0
c
f
(
x
+
h
)
−
c
f
(
x
)
h
=
c
lim
h
→
0
f
(
x
+
h
)
−
f
(
x
)
h
=
c
f
′
(
x
)
.
\begin{align*} g'(x)&=\lim_{h\to 0}\frac{g(x+h)-g(x)}{h} \\ &=\lim_{h\to 0}\frac{cf(x+h)-cf(x)}{h} \\ &=c\lim_{h\to 0}\frac{f(x+h)-f(x)}{h} \\ &=cf'(x). \end{align*}
g
′
(
x
)
=
h
→
0
lim
h
g
(
x
+
h
)
−
g
(
x
)
=
h
→
0
lim
h
c
f
(
x
+
h
)
−
c
f
(
x
)
=
c
h
→
0
lim
h
f
(
x
+
h
)
−
f
(
x
)
=
c
f
′
(
x
)
.
0
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