flexastexas
  • flexastexas
Need some help with limits
Mathematics
jamiebookeater
  • jamiebookeater
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flexastexas
  • flexastexas
http://imgur.com/a/mfEtg this is what I have so far
phi
  • phi
which question?
flexastexas
  • flexastexas
All of them. I was doing these with my dad, just want to know if I am on the right track

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phi
  • phi
Q4 looks wrong. x->0+, the curve is going down to -infty
phi
  • phi
for Q1, tan(x) as you approach pi/2 from the positive (the right side) is going to negative infinity
flexastexas
  • flexastexas
My understanding is that a when they say ->0+ they mean that approaching 0 on the positive side, what is at the y
phi
  • 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.
flexastexas
  • flexastexas
So, when a question is asking what is the limit what are they really asking?
phi
  • phi
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flexastexas
  • flexastexas
What I am seeing is you drew a line through the 0 that is intersecting the other line
flexastexas
  • flexastexas
Am I seeing it right?
phi
  • 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
phi
  • 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 \[ \lim_{x\rightarrow 0} \ln(x) = -\infty \]
flexastexas
  • flexastexas
OOOOH ok What does the + & - sign above the number being approached come into play?
phi
  • 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+
phi
  • phi
so for example, read \[ \lim_{x\rightarrow \frac{\pi}{2}^+} \] as "x approaches pi/2 from the positive (right side) of pi/2 "
flexastexas
  • flexastexas
Okay I understand Ill do some more studying. Thanks for your help

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