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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
2
x
x
−
5
f(x)=\frac{2x}{x-5}
f
(
x
)
=
x
−
5
2
x
and
g
(
x
)
=
3
x
+
5
g(x)=\frac{3}{x+5}
g
(
x
)
=
x
+
5
3
. (a) Form the function
h
(
x
)
=
(
f
+
g
)
(
x
)
h(x)=(f+g)(x)
h
(
x
)
=
(
f
+
g
)
(
x
)
and simplify your answer. (b) Calculate
lim
x
→
10
h
(
x
)
\displaystyle \lim_{x\to 10} h(x)
x
→
10
lim
h
(
x
)
, showing all necessary steps.
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