The graphs of f(x) and g(x) are shown below. Estimate limit as (x to 0) [f(x)+2]/[g(x)-3] by using L'Hospital's Rule. Explain why you can apply this rule.

Question

anonymous · Answer

attachment

loser66 · Answer

when x =0 , f(x) +2 =0, and at that point g(x) -3 =0, therefore, the expression form the form of 00 enough to apply l'hopital rule

loser66 · Answer

0/0 no 00

anonymous · Answer

lol thanks

anonymous · Answer

what will we get when we apply lh rule ?

loser66 · Answer

it's your job. I don't know , hihihihi... just know the reason why we can apply "l'hospital" rule

anonymous · Answer

we take derivative of f(x) and g(x) ?

anonymous · Answer

ok lol

loser66 · Answer

yes, f'x, g'x seperately

ranga · Answer

lim x-> 0   [f(x)+2] / [g(x)-3] = 0/0.  Apply L'H.  Differentiate top and bottom:
lim x-> 0   [f(x)+2] / [g(x)-3] = lim x-> 0 f'(x) / g'(x)  = f'(0) / g'(0)
g(x) is a 45 degree straight line.  Its slope is +1 everywhere.
So g'(0) = 1.
f(x) has a minimum at x = 0.  Therefore, f'(0) = 0  (tangent is horizontal line with slope of zero).
f'(0) / g'(0) = 0 / 1 = 0.

ranga · Answer

And the above is not an estimate.  It is an accurate limit.

anonymous · Answer

ok got it thank you