Question

I need help with the first practice problem and understanding of it.

Answer 1

11) Given,

`lim_(x\rightarrow3)(x-9)/(√(x)-3)`

To find: Evaluate.

Solution:

Multiply both numerator and denominator by the conjugate of

`√(x)+3`

Now,

`\begin{gathered} lim_(x\rightarrow3)((x-9)(√(x)+3))/((√(x)-3)(√(x)+3)) \\ =lim_(x\rightarrow3)((x-9)(√(x)+3))/((√(x))^2-(3)^2) \\ =lim_(x\rightarrow3)((x-9)(√(x)+3))/(x^-9) \\ =lim_(x\rightarrow3)(√(x)+3) \end{gathered}`

Put x = 3 in the expression.

`(√(3)+3)=√(3)(√(3)+1)`

Thus, the answer is

`√(3)(√(3)+1)`