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  3. (a) consider the function f(x)=(ex ?1)/x. use l’

(a) Consider the function f(x)=(ex ?1)/x. Use l’Hˆopital’s rule to show that lim f(x) = 1...

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Advance Math

(a) Consider the function f(x)=(ex ?1)/x.

Use l’Hˆopital’s rule to show that lim f(x) = 1 when xapproaches 0

(b) Check this result empirically by writing a program tocompute f(x) for x = 10?k, k = 1,...,15. Do your results agree withtheoretical expectations? Explain why.

(c) Perform the experiment in part b again, this time using themathematically equivalent formulation, f(x)=(ex?1)/log(ex), evaluated as indicated, with nosimplification. If this works any better, can you explain why?

Please ignore the programming part. I am interested in knowingwhy this happens.

Answer & Explanation Solved by verified expert
4.1 Ratings (709 Votes)
By LHopitals rule in any limit valueit in indeterminate form so that is 00 here we canapplyLHopitals rule so that we get it in determinedlimit valueBy this rule we can differentiate fx and gx separately andthen it is in ratio we can evaluate if still it is same    See Answer
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