## flexastexas one year ago Need some help with limits

1. flexastexas

http://imgur.com/a/mfEtg this is what I have so far

2. phi

which question?

3. flexastexas

All of them. I was doing these with my dad, just want to know if I am on the right track

4. phi

Q4 looks wrong. x->0+, the curve is going down to -infty

5. phi

for Q1, tan(x) as you approach pi/2 from the positive (the right side) is going to negative infinity

6. flexastexas

My understanding is that a when they say ->0+ they mean that approaching 0 on the positive side, what is at the y

7. phi

for Q4, x->0 means x is getting close to 0 (on the x-axis) x->0+ means we are on the positive side (as you state), and approaching x=0 at x=1 the curve is at y=0, but that is not what you want.

8. flexastexas

So, when a question is asking what is the limit what are they really asking?

9. phi

|dw:1440679872077:dw|

10. flexastexas

What I am seeing is you drew a line through the 0 that is intersecting the other line

11. flexastexas

Am I seeing it right?

12. phi

that is a sketch of the curve ln(x) it asymptotes to the y-axis (i.e never reaches the y-axis) for some background (if you have time) see https://www.khanacademy.org/math/differential-calculus/limits_topic/limits_tutorial/v/introduction-to-limits-hd

13. phi

we could make a list of numbers ln(0.1) = -2.3 ln(0.01) = -4.6 ln(0.001)= -6.9 as x in ln(x) gets closer to 0, ln(x) gets more negative, but never reaches a fixed value we say $\lim_{x\rightarrow 0} \ln(x) = -\infty$

14. flexastexas

OOOOH ok What does the + & - sign above the number being approached come into play?

15. phi

$$x \rightarrow 0^-$$ means we approach 0 from the negative side (left side) of 0 $$x \rightarrow 0^+$$ means we approach 0 from the positive side (right side) of 0 $$x \rightarrow 0$$ means we approach 0 from both sides (and to be defined, we have to get the same answer either way) notice in Q1, the tangent goes to +infinity for x->pi/2- and -infinity for x->pi/2+

16. phi

so for example, read $\lim_{x\rightarrow \frac{\pi}{2}^+}$ as "x approaches pi/2 from the positive (right side) of pi/2 "

17. flexastexas

Okay I understand Ill do some more studying. Thanks for your help