119k views
3 votes
I'm stuck on this question, any ideas? thanks

I'm stuck on this question, any ideas? thanks-example-1
User Notuo
by
8.1k points

2 Answers

3 votes

Answer:

-1/36

Explanation:

lim(x→0) [1/(6 + x) − 1/6] / x

The common denominator of the two fraction in the numerator is 6(6 + x) = 36 + 6x.

lim(x→0) [6/(36 + 6x) − (6 + x)/(36 + 6x)] / x

Combine the fractions.

lim(x→0) [(6 − 6 − x) / (36 + 6x)] / x

Simplify.

lim(x→0) [-x / (36 + 6x)] / x

Divide.

lim(x→0) -1 / (36 + 6x)

Evaluate.

-1/36

User Candino
by
8.5k points
7 votes

Answer:


\lim_(x \to 0) ((1)/(6+x)-(1)/(6))/(x)=-1/36

Explanation:

So we have the limit:


\lim_(x \to 0) ((1)/(6+x)-(1)/(6))/(x)

Let's remove the fractions in the denominator by multiplying both layers by (6+x)(6). So:


\lim_(x \to 0) ((1)/(6+x)-(1)/(6))/(x)\cdot (((6+x)(6))/((6+x)(6)))

Distribute:


=\lim_(x \to 0) ((6)-(6+x))/(x(6+x)(6))

Simplify the numerator:


=\lim_(x \to 0) (6-6-x)/(x(6+x)(6))\\=\lim_(x \to 0) (-x)/(x(6+x)(6))

Both the numerator and the denominator have an x. Cancel:


=\lim_(x \to 0) (-1)/((6+x)(6))

Direct substitution:


= (-1)/((6+0)(6))

Simplify:


=-1/36

And that's our answer.

And we're done!

User Humblelistener
by
8.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories