I dont understand the bit where it says that it goes to ln4
#Improper integral
glacial bronze
versed mossBOT
I dont understand the bit where it says that it goes to ln4
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glacial bronze
cus i thought that if x-->infinity then the bottom part is bigger than the top part
therefore it tends to 0
but my thinking is wrong
sacred axle
I dont understand the bit where it says that it goes to ln4
Well, (2t^2 + 3)^2/(t + 1)^4 for t = 0 is 4.
Oh, wait, it's for infinity.
glacial bronze
yeah
sacred axle
cus i thought that if x-->infinity then the bottom part is bigger than the top p...
No. Why? The orders of both the numerator and denominator are the same (t^4), so just compare the leading coefficients.
glacial bronze
everytime i do these type of questions i always mess up when evaluating the integral like here
glacial bronze
No. Why? The orders of both the numerator and denominator are the same (t^4), so...
wait i never done this
so i expand the 2t^2 +3
glacial bronze
and compare the 4t^4 with the t^4 on bottom?
ohhhhhhh
ok
so wait if i ever get a question i should divide everything by the highest order of the numerator?
sacred axle
Well, in general, when evaluating the limits of rational functions, you factor out the highest powers from the numerator and denominator, then cancel.
Then you're left with a power of t (in this case t^0, since the degrees of numerator and denominator are the same) and an expression with a finite nonzero limit.
glacial bronze
i sort of understand it i think
ima try dividing everything by t^4 and see what happens
1 sec
sacred axle
Just recall how you did it when studying limits.
glacial bronze
i think i sort of get it now
all other terms are bascially irrelevant since it goes it infinity and you divide by t
is this a valid way?
glacial bronze
Just recall how you did it when studying limits.
my teacher skipped over this part
he thought that we already knew it and never did it
sacred axle
Well, probably better to write the fraction in the last step as (2 + 3/t^2)^2/(1 + 1/t)^4. Still exact, but you can still see the infinitesimal terms.
sacred axle
he thought that we already knew it and never did it
Oh... Quite an important step to skip.
glacial bronze
Well, probably better to write the fraction in the last step as (2 + 3/t^2)^2/(1...
i see i will keep that in mind next time
glacial bronze
Oh... Quite an important step to skip.
yeah need to relearn it rn
but tysm
+close
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