# How do you prove that #g(x) = 1/2x# is continuous at #x=1/4#?

Please refer to the Explanation.

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To prove that g(x) = 1/2x is continuous at x=1/4, we need to show that the limit of g(x) as x approaches 1/4 exists and is equal to g(1/4).

First, let's find the limit of g(x) as x approaches 1/4:

lim(x→1/4) (1/2x) = 1/2 * (lim(x→1/4) 1/x)

Next, we evaluate the limit of 1/x as x approaches 1/4:

lim(x→1/4) 1/x = 1/(1/4) = 4

Therefore, the limit of g(x) as x approaches 1/4 is 4.

Now, let's find g(1/4):

g(1/4) = 1/2 * (1/4) = 1/8

Since the limit of g(x) as x approaches 1/4 (which is 4) is equal to g(1/4) (which is 1/8), we can conclude that g(x) = 1/2x is continuous at x=1/4.

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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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