Evaluate
X^25 ÷ X^-5
Answers
Answer:
Explanation:
There are a few ways we can tackle this- I will show an algebraic way and a more calculus-themed way:
Algebraic Way:
If we plug
5
into our expression, we immediately see that we will get indeterminate form, or
0
0
.
The key is to realize that we have a difference of squares in the numerator. This allows us to rewrite the expression as
(
x
+
5
)
(
x
−
5
)
x
−
5
Common factors cancel, and we're left with
lim
x
→
5
x
+
5
=
5
+
5
=
10
Calculus Way:
We can use L'Hôpital's rule, which says if we want to evaluate the limit of
f
(
x
)
g
(
x
)
, this equal to
lim
x
→
c
f
'
(
x
)
g
'
(
x
)
We take the derivative of our numerator and denominator expression, and evaluate the limit.
In our example,
f
(
x
)
=
x
2
−
25
⇒
f
'
(
x
)
=
2
x
g
(
x
)
=
x
−
5
⇒
g
'
(
x
)
=
1
We now have the expression
lim
x
→
5
=
2
x
1
=
2
⋅
5
=
10
Both ways, we get
10
.
Hope this helps
Step-by-step explanation:
x x question by two of the egg is equal