Pre-calc, image attached

Question

asked Dec 17, 2022 191k views

1 Answer

Duwayne · Answer 1 · 2022-12-21T16:52:53+0000

Answer:

$\lim_(x \to 7) (√(x+2)-3 )/(x-7) = (1)/(6)$

Explanation:

$\lim_(x \to 7) (√(x+2)-3 )/(x-7)$

(√(x+2)-3 )/(x-7)

$\frac{(1)/(2) (x+2)^{-(1)/(2) }}{1}$ <-- Take derivative of numerator and denominator expressions

${(1)/(2) (x+2)^{-(1)/(2) }}$ <-- Simplify

(1)/(2)((1)/(√(x+2) )) <-- Rewrite

(1)/(2)((1)/(√(7+2) )) <-- Use direct substitution and plug in the limit x=7

(1)/(2)((1)/(√(9) ))

$(1)/(2)(\frac{1}3 })$

(1)/(6)

Therefore,
$\lim_(x \to 7) (√(x+2)-3 )/(x-7) = (1)/(6)$