Finding limits from graphs
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Topic Notes
Limit is an important instrument that helps us understand ideas in the realm of Calculus. In this section, we will learn how to find the limit of a function graphically using one-sided limits and two-sided limits.
DEFINITION:
left-hand limit: limx→a−f(x)=L
We say "the limit of f(x), as x approaches a from the negative direction, equals L".
It means that the value of f(x) becomes closer and closer to L as x approaches a from the left, but x is not equal to a.
DEFINITION:
right-hand limit: limx→a+f(x)=L
We say "the limit of f(x), as x approaches a from the positive direction, equals L".
It means that the value of f(x) becomes closer and closer to L as x approaches a from the right, but x is not equal to a.
DEFINITION:
limx→af(x)=L if and only if limx→a+f(x)=L and limx→a−f(x)=L
left-hand limit: limx→a−f(x)=L
We say "the limit of f(x), as x approaches a from the negative direction, equals L".
It means that the value of f(x) becomes closer and closer to L as x approaches a from the left, but x is not equal to a.
DEFINITION:
right-hand limit: limx→a+f(x)=L
We say "the limit of f(x), as x approaches a from the positive direction, equals L".
It means that the value of f(x) becomes closer and closer to L as x approaches a from the right, but x is not equal to a.
DEFINITION:
limx→af(x)=L if and only if limx→a+f(x)=L and limx→a−f(x)=L
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