Limits of Functions?

**dark-ryder341** · October 2nd 2009, 06:11 PM

Hello everyone,

Well, our class recently started learning limits, and I'm having some troubles with two of the questions from the homework.

The first question is:

State the value of the limit of the function: f(x) = 4/5+e^(1/x)

lim f(x) for x --> 0+

I got 4/5+e^(1/0+) = 4/5+e^(infinity) = 4/5+infinity....I said the answer was infinity, but that was wrong.

The other question involves finding the limits of functions that have square roots in them. I was wondering if there's any 'general' way of solving those sorts of functions, since I have four of those questions, and I'm unsure of how to go about those.

Anyhow, the second question is: Find the limit for:

lim for x --> -infinity squareroot(9x^6-x)/x^3+6

I really have no idea how to go about this question, so any help is greatly appreciated!

**DeMath** · October 2nd 2009, 06:22 PM

Originally Posted by dark-ryder341

Hello everyone,

Well, our class recently started learning limits, and I'm having some troubles with two of the questions from the homework.

The first question is:

State the value of the limit of the function: f(x) = 4/5+e^(1/x)

lim f(x) for x --> 0+

I got 4/5+e^(1/0+) = 4/5+e^(infinity) = 4/5+infinity....I said the answer was infinity, but that was wrong.

Maybe you given this function $f\left( x \right) = \frac{4}{{5 + {e^{1/x}}}}$ ??

**dark-ryder341** · October 2nd 2009, 06:27 PM

Yes, that was the function I was given. Sorry, I don't know how to write it out properly like that. I'm just not sure how to solve it...

**DeMath** · October 2nd 2009, 06:34 PM

Originally Posted by dark-ryder341

Yes, that was the function I was given. Sorry, I don't know how to write it out properly like that. I'm just not sure how to solve it...

Then

$f\left( x \right) = \frac{4}{{5 + {e^{1/x}}}}$

$\mathop {\lim }\limits_{x \to {0^ + }} f\left( x \right) = \mathop {\lim }\limits_{x \to {0^ + }} \frac{4}{{5 + {e^{1/x}}}} = \frac{4}<br /> {{5 + {e^\infty }}} = \frac{4}{\infty } = 0.$

**DeMath** · October 2nd 2009, 06:39 PM

Originally Posted by dark-ryder341

Hello everyone,

Well, our class recently started learning limits, and I'm having some troubles with two of the questions from the homework.

The other question involves finding the limits of functions that have square roots in them. I was wondering if there's any 'general' way of solving those sorts of functions, since I have four of those questions, and I'm unsure of how to go about those.

Anyhow, the second question is: Find the limit for:

lim for x --> -infinity squareroot(9x^6-x)/x^3+6

I really have no idea how to go about this question, so any help is greatly appreciated!

$\mathop {\lim }\limits_{x \to - \infty } \frac{{\sqrt {9{x^6} - x} }}<br /> {{{x^3} + 6}} = \mathop {\lim }\limits_{x \to - \infty } \frac{{\left| {{x^3}} \right|\sqrt {9 - \frac{1}{{{x^5}}}} }}{{{x^3}\left( {1 + \frac{6}<br /> {{{x^3}}}} \right)}} = - \mathop {\lim }\limits_{x \to - \infty } \frac{{\sqrt {9 - \frac{1}{{{x^5}}}} }}{{1 + \frac{6}{{{x^3}}}}} = - \frac{{\sqrt {9 + 0} }}{{1 - 0}} = - 3.$

**dark-ryder341** · October 2nd 2009, 07:28 PM

Thanks very much for your help! Also, I was wondering for this question:

How were the values of f(x) obtained? I tried plugging in the x values into the function, but got different numbers.

**redsoxfan325** · October 2nd 2009, 08:42 PM

Are you sure you didn't round at all in the middle? I'm plugging in x and getting out what they have for f(x).

**dark-ryder341** · October 2nd 2009, 09:33 PM

Nope, I didn't round...when I plugged in 1 for x, I got 4.582575695...maybe I'm entering it in my calculator wrong?

squareroot(1+25-5/1) ?

**mr fantastic** · October 2nd 2009, 09:37 PM

Originally Posted by dark-ryder341

Nope, I didn't round...when I plugged in 1 for x, I got 4.582575695...maybe I'm entering it in my calculator wrong?

squareroot(1+25-5/1) ?

More brackets are needed. Perhaps making correct use of them will give you the correct answer.

(Sqrt(1 + 25) - 5)/1

etc.

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