lim x -3 sqrt 2x+22 -4 x+3
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The limit equals
−
4
.
Explanation:
If we try evaluating into the initial expression, we get
L
=
0
0
=
∞
So we can use l'Hopitals Rule.
L
=
lim
x
→
−
3
1
−
2
2
√
2
x
+
22
L
=
lim
x
→
−
3
1
−
1
√
(
2
x
+
22
)
L
=
lim
x
→
−
3
−
√
2
x
+
22
Now we can evaluate directly:
L
=
−
√
2
(
−
3
)
+
22
L
=
−
√
16
L
=
−
4
If we do a graphical check, we obtain the same result.
graph{(x + 3)/(4 - sqrt(2x + 22)) [-10, 10, -5, 5]}
Hopefully this helps!
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