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Let-s-R-z-define-as-R-z-pi-0-z-f-2-t-dt-2pi-0-z-f-t-1-f-1-t-2-dt-and-both-integral-0-f-2-t-dt-0-f-t-1-f-1-t-2-dt-lim-z-

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Question Number 214511 by issac last updated on 11/Dec/24
Let′s R(z) define as R(z)=((π ∫_0 ^( z) f^2 (t)dt)/(2π ∫_0 ^( z) f(t)(√(1+(f^((1)) (t))^2 ))dt)) and both integral ∫_0 ^( ∞) f^( 2) (t)dt , ∫_0 ^( ∞) f(t)(√(1+(f^((1)) (t))^2 ))dt =∞ lim_(z→∞) ((π ∫_0 ^( z) f^( 2) (t)dt)/(2π ∫_0 ^( z) f(t)(√(1+(f^((1)) (t))^2 ))dt)) =lim_(z→∞) ((π f(z))/(2π (√(1+(f^((1)) (z))^2 )))) ..??
Let′sR(z)defineasR(z)=π∫0zf2(t)dt2π∫0zf(t)1+(f(1)(t))2dtandbothintegral∫0∞f2(t)dt,∫0∞f(t)1+(f(1)(t))2dt=∞limz→∞π∫0zf2(t)dt2π∫0zf(t)1+(f(1)(t))2dt=limz→∞πf(z)2π1+(f(1)(z))2..??

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