Hi! I'm a bit confused with logorithims and exponentials since I was absent for most lessons when it was taught and hoping that you guys could help me clear up some stuff.
Sure thing!
a) Is something like ex or xex always greater than 0?
\(e^x>0\) for all values of \(x\), but \(xe^x\) can be less than or equal to zero depending on the value of \(x\)
b) Is there a rule that e-x (or to the power of negative anything) cannot equal to 0?
Yep, \(e^{-x}\neq0\) just like \(e^x\neq0\)
c) I did this question and got the answer but I'm not sure why it is?
 \\<br />= \lim_{x\to\infty} (3-e^{-x}) \\<br />= 3)
Since x is approaching infinity I put in e-9999 etc. in the calculator which gave a 0, which is why I presumed the answer was 3 although I'm still a bit confused by it all
So remember a limit just looks at what happens to a function as it approaches a given value. In this case, what happens as \(x\) gets really large. If you sketch a graph of \(e^{-x}\), you'll see it approaches zero for large values of \(x\). Hence, the value of the limit is 3, since that exponential term will vanish, if that makes sense?
d) Similarly, there's also this question which asks you to solve for x
 > 0 )
That exponential term can never equal zero, and will always be positive, so the inequality becomes completely reliant on the bracketed term:
I'm also wondering if anyone knows whether Fitzpatrick (both 2/3u books) or Cambridge (just the 3U one, I have the 2U book as well but I pressume 2u is integrated/incorporated into the 3u book?) is the better option?
Thank you in advance!
Cambridge is the better option for questions imo, more challenging exercises that will better prepare you for exams
both explain things quite well, though Cambridge takes a more theoretical approach that is a little tougher to comprehend for a lot of people
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