Question

59. If $\lim _{x \rightarrow 1} \frac{f(x)-8}{x-1}=10,$ find $\lim _{x\rightarrow1}f(x)\text{.}$

Answer 1

Answer:

$\large\lim_{x\rightarrow 1} f\left( x\right)=8$

Step-by-step explanation:

$\lim_{x\rightarrow 1} \frac{f\left( x\right) -8}{x-1} =10$

$\lim_{x\rightarrow 1} f\left( x\right) -8=10\times \lim_{x\rightarrow 1}\left( x-1\right)$

$\lim_{x\rightarrow 1} f\left( x\right) -8=10\times\left( (1)-1\right)$

$\lim_{x\rightarrow 1} f\left( x\right) -8=10\times\left( 0\right)=0$

$\lim_{x\rightarrow 1} f\left( x\right) -8=0$

$\lim_{x\rightarrow 1} f\left( x\right) =8$