Prove the following forms of l'Hôpital's Rule (none requiring any essentially new reasoning) (a) If lim f(x) lim f(x)/g(x) -lim g(x) 0, and lim f,(D/g'(x) then 1, = = x->a+ 1 (and similarly for limits from below) x→a (b) If lim f(r) - lim g(x) - 0, and lim f"(x)/g'(x)o, then a is replaced limf(x)/g(x)-oo (and similarly for-00, or if x (c) If l linng(x) 0, and lin/(xyg'(x) -1, then lim f(x) = = xOXO lim f(x)/s(a) - / (and similarly for -oo). Hint: Consider lim f(l/x)/g(1/x) x→0+ (d) Iflimo f(x) 0, and xin of,(x)/g'(x) -x-mo g(x) - o0, then = xOXO lim f(x)/g(x)=

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A:

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A: In general,  this is false statement.    Answer : False     Reason is below:

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Q: ل بريال

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