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flexastexas
 one year ago
Need some help with limits
flexastexas
 one year ago
Need some help with limits

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flexastexas
 one year ago
Best ResponseYou've already chosen the best response.1http://imgur.com/a/mfEtg this is what I have so far

flexastexas
 one year ago
Best ResponseYou've already chosen the best response.1All of them. I was doing these with my dad, just want to know if I am on the right track

phi
 one year ago
Best ResponseYou've already chosen the best response.2Q4 looks wrong. x>0+, the curve is going down to infty

phi
 one year ago
Best ResponseYou've already chosen the best response.2for Q1, tan(x) as you approach pi/2 from the positive (the right side) is going to negative infinity

flexastexas
 one year ago
Best ResponseYou've already chosen the best response.1My understanding is that a when they say >0+ they mean that approaching 0 on the positive side, what is at the y

phi
 one year ago
Best ResponseYou've already chosen the best response.2for Q4, x>0 means x is getting close to 0 (on the xaxis) 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
 one year ago
Best ResponseYou've already chosen the best response.1So, when a question is asking what is the limit what are they really asking?

flexastexas
 one year ago
Best ResponseYou've already chosen the best response.1What I am seeing is you drew a line through the 0 that is intersecting the other line

flexastexas
 one year ago
Best ResponseYou've already chosen the best response.1Am I seeing it right?

phi
 one year ago
Best ResponseYou've already chosen the best response.2that is a sketch of the curve ln(x) it asymptotes to the yaxis (i.e never reaches the yaxis) for some background (if you have time) see https://www.khanacademy.org/math/differentialcalculus/limits_topic/limits_tutorial/v/introductiontolimitshd

phi
 one year ago
Best ResponseYou've already chosen the best response.2we 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
 one year ago
Best ResponseYou've already chosen the best response.1OOOOH ok What does the + &  sign above the number being approached come into play?

phi
 one year ago
Best ResponseYou've already chosen the best response.2\( x \rightarrow 0^ \) 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
 one year ago
Best ResponseYou've already chosen the best response.2so for example, read \[ \lim_{x\rightarrow \frac{\pi}{2}^+} \] as "x approaches pi/2 from the positive (right side) of pi/2 "

flexastexas
 one year ago
Best ResponseYou've already chosen the best response.1Okay I understand Ill do some more studying. Thanks for your help
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