Find the limit
(calculus)

I believe also equals 0.

Step-by-step explanation:

We know that g(x) has to be greater than or equal to 0. That means f(x) has to be smaller than g(x) or equal to 0.

If we plug in any value of x, f(x) will be positive because of the absolute value. The only way we are going to get f(x) smaller than g(x) or equal to g(x) is to have very small fractions.

Therefore, if , then because f(x) must be smaller or equal to 0 as well.

Step-by-step explanation:

The other user posted a great answer, but I would like to show you a more mathematical way!

We have .

By the definition of absolute value, this is the same as saying:

For the right, we can divide both sides by -1 to acquire:

We can now combine them. This yields:

Now, we can use the Squeeze Theorem (a.k.a. Pinch or Sandwich Theorem). The Squeeze Theorem posits that if we have:

And:

Then the following must be true:

We have:

And we know that:

Then it follows that:

Therefore, by using the Squeeze Theorem, we can conclude that:

And we're done!

the answer is 200

step-by-step explanation:

the way the question is worded, it seems to imply the $264 interest is simple interest, not compound interest.

the simple interest for 2 years is $264; the simple interest for 1 year is $132.

$132 interest on a $600 investment means an interest rate of (132/600)*100 = 22%.

the value of $200 at 22% interest compounded annually for three years is

200%281.22%29%5e3

the amount of interest is that value, minus the original $200.