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let-f-x-x-2x-sht-t-dt-1-calculate-f-x-2-find-lim-x-0-f-x-




Question Number 31506 by abdo imad last updated on 09/Mar/18
let f(x)=∫_x ^(2x)  ((sht)/t)dt  1) calculate f^′ (x)  2) find lim_(x→0)  f(x) .
letf(x)=x2xshttdt1)calculatef(x)2)findlimx0f(x).
Commented by abdo imad last updated on 12/Mar/18
1)f^′ (x)=2 ((sh(2x))/(2x)) −((shx)/x) = ((sh(2x)−shx)/x) .  2) ∃ c ∈]x,2x[ /f(x)=sh c ∫_x ^(2x)  (dt/t)=sh(c)ln(2)_(x→0)  →0
1)f(x)=2sh(2x)2xshxx=sh(2x)shxx.2)c]x,2x[/f(x)=shcx2xdtt=sh(c)ln(2)x00

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