Question

cho f(x) là 1 đa thức thoa man \(\lim\limits_{x\rightarrow1}\dfrac{f\left(x\right)-16}{x-1}=24\). tính \(\lim\limits_{x\rightarrow1}\dfrac{f\left(x\right)-16}{\left(x-1\right)\left(\sqrt{2f\left(x\right)+4}+6\right)}\)

Answer 1

\(\lim\limits_{x\rightarrow1}\dfrac{f\left(x\right)-16}{x-1}\) hữu hạn nên \(f\left(x\right)-16=0\) có nghiệm \(x=1\)

\(\Rightarrow f\left(1\right)=16\)

\(\lim\limits_{x\rightarrow1}\dfrac{f\left(x\right)-16}{x-1}.\dfrac{1}{\sqrt{2f\left(x\right)+4}+6}=24.\dfrac{1}{\sqrt{2.16+4}+6}=2\)