Question
Use properties of limits and algebraic methods to find the limit, if it exists. lim h 0 2( x + h ) 2 2 x
Use properties of limits and algebraic methods to find the limit, if it exists.
lim
h0
2(x+h)22x2
h
Notice that whenh= 0, the denominator oflim
h0
2(x+h)22x2
h
is zero.
Recall that if the numerator is also zero whenh= 0, the limit has the indeterminate form0
0
andhis a common factor of the numerator and denominator.
To determine if the numerator is zero whenh= 0, replacehwith 0 in the numerator of the limit and simplify.
2(x+h)22x2=2(x+ 0)22x2
=
Thus,lim
h0
2(x+h)22x2
h
---Select---
has
does not have
the indeterminate form0
0
ath= 0
andh
---Select---
is
is not
a common factor of the numerator and denominator.
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