# Let f be a function defined by: ?

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Let f be a function defined by:

State the domain of "f" and find the value(s) of a for which "f" is a continuous function.

Let f be a function defined by:

State the domain of "f" and find the value(s) of a for which "f" is a continuous function.

The Domain of the Function is:

or

The value of a is

So how do we do that? Well we have different ways of going about this. The first, and simplest, is to graph the function and see what happens at the value.

graph{(sqrt(7x+2)-sqrt(6x+4))/(x-2) [1.6815, 2.2657, -0.0507, 0.2413]}

I want to rationalize the numerator, so that I get rid of the square roots up there. So I'll multiply by the conjugate.

Now, let's simplify it.

Now, we can combine like terms and simplify even further.

Now, just plug in 2, and get:

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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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- What is the discontinuity of the function #f(x)=(3x^2+x-4)/(x-1)#?
- What is the limit of #(1+1/x)^x# as x approaches infinity?

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