Question

Find the limit of (sqrt(x+5)-4)/(x-11) as x approaches 11

Answer 1

`\lim\limits_(x\to11)(√(x+5)-4)/(x-11)=\lim\limits_(x\to11)((√(x+5)-4)(√(x+5)+4))/((x-11)(√(x+5)+4))\\\\=\lim\limits_(x\to11)((√(x+5))^2-4^2)/((x-11)(√(x+5)+4))=\lim\limits_(x\to11)(x+5-16)/((x-11)(√(x+5)+4))\\\\=\lim\limits_(x\to11)(x-11)/((x-11)(√(x+5)+4))=\lim\limits_(x\to11)(1)/(√(x+5)+4)=(1)/(√(11+5)+4)\\\\=(1)/(√(16)+4)=(1)/(4+4)=(1)/(8)\\\\Answer:\ d.\ (1)/(8)`