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

Question

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

Answer 1

`\large\lim_(x\rightarrow 1) f\left( x\right)=8`

Explanation:

`\lim_(x\rightarrow 1) (f\left( x\right) -8)/(x-1) =10`

`\lim_(x\rightarrow 1) f\left( x\right) -8=10* \lim_(x\rightarrow 1)\left( x-1\right)`

`\lim_(x\rightarrow 1) f\left( x\right) -8=10*\left( (1)-1\right)`

`\lim_(x\rightarrow 1) f\left( x\right) -8=10*\left( 0\right)=0`

`\lim_(x\rightarrow 1) f\left( x\right) -8=0`

`\lim_(x\rightarrow 1) f\left( x\right) =8`