# How do you use the formal definition of a limit to find #lim 4x -1# as x approaches 2?

Let:

Evaluate now:

which proves that:

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To use the formal definition of a limit to find lim 4x - 1 as x approaches 2, we need to evaluate the expression 4x - 1 as x gets arbitrarily close to 2.

According to the formal definition of a limit, for any positive value ε (epsilon), there exists a positive value δ (delta) such that if 0 < |x - 2| < δ, then |(4x - 1) - L| < ε, where L is the limit we are trying to find.

To find the limit, we substitute the value of x into the expression 4x - 1 and simplify it. In this case, as x approaches 2, we substitute x = 2 into the expression:

lim 4x - 1 as x approaches 2 = 4(2) - 1 = 8 - 1 = 7.

Therefore, the limit of 4x - 1 as x approaches 2 is 7.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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