Answer:
3
Step-by-step explanation:
lim(t→∞) [t ln(1 + 3/t) ]
If we evaluate the limit, we get:
∞ ln(1 + 3/∞)
∞ ln(1 + 0)
∞ 0
This is undetermined. To apply L'Hopital's rule, we need to rewrite this so the limit evaluates to ∞/∞ or 0/0.
lim(t→∞) [t ln(1 + 3/t) ]
lim(t→∞) [ln(1 + 3/t) / (1/t)]
This evaluates to 0/0. We can simplify a little with u substitution:
lim(u→0) [ln(1 + 3u) / u]
Applying L'Hopital's rule:
lim(u→0) [1/(1 + 3u) × 3 / 1]
lim(u→0) [3 / (1 + 3u)]
3 / (1 + 0)
3
Answer:
$461.15
Step-by-step explanation:
Total amount of items:
Add all the prices together
399.99+24.99+5=429.98
Sales tax:
Convert 7.25% to a decimal
7.25/100=0.0725
Multiply the total by the decimal
429.98*0.0725=31.17355
Final cost:
Add the sales tax and total amount
429.98+31.17355=461.15355
Round to the nearest cent/hundreth
$461.15
Hope this helps! :)
