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Lirrick007
@Lirrick007
October 2021
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lim[tex] \frac{x-5}{2- \sqrt{x-1} } [/tex]
x→5
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kirichekov
Verified answer
Lim((x-5)/(2-√(x-1))=(5-5)/(2-√(5-1))=0/0
x->5
lim((x-5)/(2-√(x-1))=lim((x-5)*(2+√(x-1)))/((2-√(x-1))*(2+√(x-1))=
x->5 x->5
lim((x-5)*((2-√(x-1)))/(2²-(√(x-1))²)=lim((x-5)*(2+√(x-1)))/(4-x+1))=
x->5 x->5
lim((x-5)*(2+√(x-1))/(x-5))=lim(2+√x-1))=2+√(5-1)=2+2=
4
x->5 x->5
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Answers & Comments
Verified answer
Lim((x-5)/(2-√(x-1))=(5-5)/(2-√(5-1))=0/0x->5
lim((x-5)/(2-√(x-1))=lim((x-5)*(2+√(x-1)))/((2-√(x-1))*(2+√(x-1))=
x->5 x->5
lim((x-5)*((2-√(x-1)))/(2²-(√(x-1))²)=lim((x-5)*(2+√(x-1)))/(4-x+1))=
x->5 x->5
lim((x-5)*(2+√(x-1))/(x-5))=lim(2+√x-1))=2+√(5-1)=2+2=4
x->5 x->5