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Question-66518




Question Number 66518 by Masumsiddiqui399@gmail.com last updated on 16/Aug/19
Commented by mathmax by abdo last updated on 16/Aug/19
let f(x)=((x(√x)−a(√a))/(x−a))   cha7gement x−a=t give  lim_(x→a) f(x) =lim_(t→0)    (((t+a)(√(t+a))−a(√a))/t)  =lim_(t→0)    (((t+a)^3 −a^3 )/(t((t+a)(√(t+a)) +a(√a))))   =lim_(t→0)     ((t^3  +3t^2 a +3ta^2 )/(t{(t+a)(√(t+a))+a(√a)))) =lim_(t→0)  ((t^2  +3at +3a^2 )/((t+a)(√(t+a)) +a(√a)))  =((3a^2 )/(2a(√a))) =(3/2)(√a)
letf(x)=xxaaxacha7gementxa=tgivelimxaf(x)=limt0(t+a)t+aaat=limt0(t+a)3a3t((t+a)t+a+aa)=limt0t3+3t2a+3ta2t{(t+a)t+a+aa)=limt0t2+3at+3a2(t+a)t+a+aa=3a22aa=32a
Commented by Tony Lin last updated on 16/Aug/19
lim_(x→a) ((x(√x)−a(√a))/(x−a))  =lim_(x→a) ((x^(3/2) −a^(3/2) )/(x−a))   =lim_(x→a) (((3/2)x^(1/2) )/1)  =(3/2)(√a)
limxaxxaaxa=limxax32a32xa=limxa32x121=32a

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