Michael12901
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13b):
For 21 b) use the fact that e^(-x) is decreasing on [0,1] to get the inequality and the integrand is non negative in that same domain to get,
For 21 b) use the fact that e^(-x) is decreasing on [0,1] to get the inequality and the integrand is non negative in that same domain to get,
the rest is trivial
How do u get the first line? x>=t. I understand the rest13b):
13e):
From a) and b),
Integrating both sides from 0 to x with respect to t,
but thats just my attempt im sure there are better ways to do it lol
its an assumption we have to make since otherwise we would be integrating over the asymptote, which will lead to a divergent integral.How do u get the first line? x>=t. I understand the rest
wait no lemme think this over this is wrongits an assumption we have to make since otherwise we would be integrating over the asymptote, which will lead to a divergent integral.
Also how do u deal with the e at the front of the expression in the middle? Because presumably u need to multiply the whole inequality by e as well.For 21 b) use the fact that e^(-x) is decreasing on [0,1] to get the inequality and the integrand is non negative in that same domain to get,
the rest is trivial
that middle term is simply just e - S_nAlso how do u deal with the e at the front of the expression in the middle? Because presumably u need to multiply the whole inequality by e as well.
Thanks btw ur help v much appreciated.
Yeah but the integral in the middle (the one with e^(-x) has an e in front of the whole integral which u haven't accounted for in the rightmost integral (in the inequality). Cos presumably that e makes the middle integral larger and I don't understand how it can be smaller than the rightmost one which doesn't have an e multiplied to itthat middle term is simply just e - S_n
for the other question im not too sure theres probably some deeper geometric interpretation behind it but i havent encountered enough functions defined as integrals to grasp it fully.
in the full working out i would have,Yeah but the integral in the middle (the one with e^(-x) has an e in front of the whole integral which u haven't accounted for in the rightmost integral (in the inequality). Cos presumably that e makes the middle integral larger and I don't understand how it can be smaller than the rightmost one which doesn't have an e multiplied to it
Ah yes ty so muchin the full working out i would have,
as e < 3
sorry for any confusion i didnt actually do this question i kinda just glanced at it lol
Yes. If I integrate from (say) to then I know that .Ah yes ty so much
Also for the x>= t matter, could it be because in part c) we're integrating a function in terms of t over the bounds 0 to x. Meaning that 0<= t <= x?? I've seen that logic used in some questions.