This week in calculus we learned about line tangents, we did more advanced derivatives, and we also condensed logs. I didn’t have any problems with solving the logs but I kind of forgot how to condense logs. I can’t belive I forgot how to do logs. O.o I’m pretty sure I grasp the arc equations such as: [arcsin], [arctan], and etc., but I still have trouble with derivatives kind of because I always stop to earlier or mess up on my algerbra but that’s something I have to practice. I also don’t understand how to use (e) fully. Some problems that will really help me out if:
Just condense the problem, #32 last week’s homework.1) 2[lnx-ln(x+1)-ln(x-1)] and
Find an equation of the tangent line #50 last week’s homework.2) y= e-2x+x^2, (2, 1) .
Other than everything we learned; this week was pretty easy if you ask me.
Well I have to do a lot of studying and extra work but with a few examples like this I should be able to learn from what I know and what everyone helps me out with.
I don’t know if I’m supposed to be asking about this because it’s not from last week but for vertical and horizontal asymptotes . I understand vertical asymptotes but I don’t know how to get horizontal.
Like for:
3/x^2-4 you get 3/(x-2)(x+2)
Which gives you vertical asymptotes at x=2, and x=-2but I don’t know how to find the Horizontal ones
Thanks I hope I was able to ask that.
Mabile
Subscribe to:
Post Comments (Atom)
To find horizontal asymptotes, you use 3 rules.
ReplyDeleteIf the degree of the top is larger than the degree of the bottom, there is none.
If the degree of the top is smaller than the degree of the bottom, it is at y=0.
If the degrees are equal, you divided the leading coefficients.
So for
3
-----
(x-2)(x+2)
The degree of the top is smaller, so the horizontal asymptote is at y=0.
if you want to find horizontal asymptotes make sure you know that its related to the y axis and also if the top is larger than the bottom there is none. if its smaller than the top its 0 and if they are equal you divide.....i hope it helps
ReplyDeleteokayy so those three rules that john was
ReplyDeletetalking about, they're in our intro to calc
notes from last year if you still have those, if not you can look at mine if you need to.
for the rule where the degree on top is greater that the degree on bottom, there is only no horizontal asymptote because in that case, Y= infinity and you cannot have a horizontal asymptote if y=infinity, but thats only true with horizontal so be careful not to try to apply that to other things.
i actually know this. like everyone else said if the leading coefficient's exponents is larger than the bottoms it is infinity. if it is equal you to the top's leading coefficient over the bottoms. and if the bottom's is smaller than the top it is 0. easy stuff :)
ReplyDeleteso i know this :)
ReplyDeleteFirst, make sure you know horizontal asymptotes are y=.
Then know that if you get infinity it is not a horizontal asymptote because that cannot exist.
There are three rules for finding them:
If the degree of the top equals the degree of the bottom you take the top's coefficient over the bottom.
Ex: x^3 + 4x^2 +2x - 1/4x^3 + 1 would give you a horizontal asymptote at y=1/4
If the degree of the top is larger that the degree of the bottom it is infinity.
Ex: x^2 + 1/x. But, if y=infinity it is not a horizontal asymptote because you cannont have that.
If the degree of the top is smaller than the degree of the bottom it is 0.
Ex: x/x^2-5 would give you a horizontal asymptote at y=0.
hey, just remember that for horizontal aymptotes, you use three rules.
ReplyDelete1. If the degree on the top is bigger than the degree on the bottom the answer is infinity.
2. If the degrees are the same, then you divide the coefficients.
3. If the degree on the top is smaller than the degree on the bottom then the answer is zero.
hope this helps!
For horizontal asymtopes, you take the limit as x approaches infiniti. When there is a fraction something like (x^2 + 3x - 2/x - 4) you have to look at the exponents at the top of the fraction and at the bottom.
ReplyDeleteIf the highest exponent (degree) is greater than the degree of the bottom, the horizontal asymtope is infiniti. This means there is no asymtope, because there can be no asymptope at infiniti.
If the degree of the bottom is greater than the degree at the top, the answer is zero.
If the degrees are the same, you make a fraction out of the coefficient in the front of the x.
EX: (3x^2 + 4x + 4/2x^2 - 16)
the answer would be 3/2 because the exponents at the top and the bottom match.
Remember when writing a horizontal asymtope, the answer is never simply the number. It's y=the number.
All you have to do is look at the degrees of both polynomial equations. And If the bottom equals zero there is none. If degree of top is the same as the bottom its the coefficients.
ReplyDelete