I need some help answering this question:f(x)=cosh(x)sinh(x)−1xfind the limit of f(x) as x tends to 0 by writing f(x) as a quotient of two powers series.I have so far:(x(1+x22!+x44!+…))−(x+x33!+…)x(x+x33!+…)=(x+x32!+x54!+…)−(x+x33!+…)(x2+x43!+…)but I don't know how to reduce this further.

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I need some help answering this question:f(x)=cosh(x)sinh(x)−1xfind the limit of f(x) as x tends to 0 by writing f(x) as a quotient of two powers series.I have so far:(x(1+x22!+x44!+…))−(x+x33!+…)x(x+x33!+…)=(x+x32!+x54!+…)−(x+x33!+…)(x2+x43!+…)but I don&#039;t know how to reduce this further.

Cheryl King · Accepted Answer

We have that  limx→0sinh(x)cosh(x)−1x=limx→0(x(1+x22!+x44!+…))−(x+x33!+…)x(x+x33!+…)  =limx→0(x+x32!+x54!+…)−(x+x33!+…)(x2+x43!+…)=limx→0(x32!+x54!+…)−(x33!+…)(x2+x43!+…)  =limx→0(x2!+x34!+…)−(x3!+…)(1+x23!+…)=0

RizerMix · Accepted Answer

(x(1+x22!+x44!+…))−(x+x33!+…)x(x+x33!+…) =(x+x32!+x54!+…)−(x+x33!)x2+x43!+… =(x32!+x54!+…)−(x33!+…)x2+x43!+… =(x2!+x34!+…)−(x3!+…)1+x23!+…→01

alenahelenash · Accepted Answer

Reduce to the same denominator and use LHospital:

I need some help answering this question: f(x)=\frac{\cosh(x)}{\sinh(x)}-\frac 1x find the limit

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