Question

Evaluate lim x approaches to 2 : (sqrt(6-x)-2)/(sqrt(3-x)-1)

Answer 1

The answer is "0.5".

Explanation:

Given:

`\to \lim_(x\to 2) ((√((6-x))-2))/((√((3-x))-1))\\\\ \to \lim_(x\to 2) ((d(√((6-x))-2))/(dx))/(((√((3-x))-1))/(dx))\\\\`

`\to \lim_(x\to 2) ((-1)/(2√((6-x)) ))/((-1)/(2√((3-x))))\\\\`

`\to \lim_(x\to 2) (√(3-x))/(√(6-x))\\\\ \to (√(3-2))/(√(6-2))\\\\ \to \frac{√(1)} {√(4)}\\\\ \to (1)/(2)\\\\ \to 0.5`