Maths question
Hi, please could I have some help on this question? For finding the range in part c, if I’m solving ln(x)-2>0 shy does the ms says 0<a<e^2? Shouldn’t it be a>e^2?
Thank you!
Thank you!
Reply 1
13
Original post
by anonymous56754Hi, please could I have some help on this question? For finding the range in part c, if I’m solving ln(x)-2>0 shy does the ms says 0<a<e^2? Shouldn’t it be a>e^2?
Thank you!
Thank you!
Reply 2
21
Original post
by anonymous56754You could just sub a value like a=e to understand it, but for the function to be positive, the numerator and denominator should have the same sign? So you want to exclude those values where the signs are different.
Reply 3
13
Original post
by mqb2766You could just sub a value like a=e to understand it, but for the function to be positive, the numerator and denominator should have the same sign? So you want to exclude those values where the signs are different.
Reply 4
21
Original post
by anonymous56754So what inequalities should I solve?
A bit like the other question youre asking about, its easier to have some insight about the function and solve some simple equations, rather than jumping to inequalities and not really unerstanding what youre doing.
So the numerator and denominator are increasing functions as ln(x) is increasing and the - c part of both just shift it down a bit. So both the numerator and denominator start at -inf when x=0 and pass through y=0 at some point and become positive. So the function g(x) will start and end positive and will be negative between the two values where the numerator and denominator equal zero. So, fairly trivially, solve
numerator = 0
denominator = 0
and reason as above. Question part a) already gives one value and the other is similar. Id sketch the numerator, denominator and g(x) for practice, noting the vertical asymptote in question part a) for g(x).
(edited 10 months ago)
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