# How do you prove that the function #1/x# is continuous at x=1?

See the Explanation.

So, in our case, we have,

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To prove that the function 1/x is continuous at x=1, we can use the definition of continuity. A function is continuous at a point if the limit of the function as x approaches that point exists and is equal to the value of the function at that point.

In this case, we need to evaluate the limit of 1/x as x approaches 1.

lim(x→1) 1/x = 1/1 = 1

Since the limit of 1/x as x approaches 1 is equal to 1, and the value of the function at x=1 is also 1, we can conclude that the function 1/x is continuous at x=1.

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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.

- How do you find the limit of #sin (x^2)/sin^2(2x)# as x approaches 0?
- How do you find the limit #lim_(x->-4)(x^2+5x+4)/(x^2+3x-4)# ?
- How do you find the limit of #(3x^2-x-10)/(x^2+5x-14)# as x approaches 2?
- How do you evaluate the limit #(x^2-25)/(x+5)# as x approaches #-5#?
- How do you find the limit of # (4t – 2t)/(t) # as t approaches 0?

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