Sunday

January 25, 2015

January 25, 2015

Posted by **Momo** on Monday, February 15, 2010 at 2:17pm.

lim {[1/(2+x)]-(1/2)}/x as x->0

How do you remove the complex fraction???

(or just complex fractions in general, I have trouble with them...)

Thank you!

- Calculus (repost) -
**drwls**, Monday, February 15, 2010 at 3:14pmThat is not a complex fraction in the sense of being a complex number (1.e., containing the square root of -1).

As x-> 0, 1/(2+x) behaves like (1/2)[1/[1 + (x/2)] = (1/2)[1 - (x/2)]

Subtract 1/2 from that, divide by x, and you have

(-x/4)/x = -1/4

You could also use L'Hopital's rule to get the limit, but I don't know if you have learned that yet. It says that the limit is the same as the limit of the ratio of the derivatives of the numerator and denominator, which is

Lim -(1/(2+x))^2 = -1/4

x->0

**Answer this Question**

**Related Questions**

Mathematics - Can someone explain to me how to solve complex fractions as if I ...

Calculus - Find the limits: lim {[1/(2+x)]-(1/2)}/x as x->0 lim (e^-x)cos x ...

Calculus - Find the limit. lim 5-x/(x^2-25) x-->5 Here is the work I have so ...

algebra - Can someone please help me with these problems? Please and thank you. ...

5th grade Language Arts - I need help classifying sentences (compound, complex, ...

Quick english help - Please check & see if I classified these sentences as ...

pre-calculus - find the complex zeros of the polynomial function. write F in the...

Pre-Calculus - I'm having trouble understanding how to do complex fractions.. My...

Calculus - I have two similar problems that I need help completing. Please show ...

Calculus--complex numbers - the complex number Z satisfies Z/(Z+4)= 3+2i Find Z...