Answer:
Attached please find answer
Step-by-step explanation:
= (x² + x - 42) / (x - 6)
= [x² + (7x - 6x) - 42] / (x - 6)
= [x² + 7x - 6x - 42] / (x - 6)
= [(x² + 7x) - (6x + 42)] / (x - 6)
= [x(x + 7) - 6(x + 7)] / (x - 6)
= [(x + 7)(x - 6)] / (x - 6)
= x + 7 → when x approches 6
= 6 + 7
= 13
Other method:
Lim (x² + x - 42) / (x - 6)
x→ 6
When x → 6, there is an indeterminate expression because: 6 - 6 = 0
Do you know the l'Hôpital's rule, when x → a:
Lim [ f(x) / g(x) ] = Lim [ f'(x) / g'(x) ]
f(x) = x² + x - 42
f'(x) = 2x + 1
g(x) = x - 6
g'(x) = 1
= f'(x) / g'(x)
= (2x + 1)/1
= 2x + 1 → when x approches 6
= 12 + 1
= 13
