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:
A and C
Step-by-step explanation:
Move all terms to the left side and set equal to zero. Then set each factor equal to zero
Answer:
C/d = 31.4/10
Step-by-step explanation:
We know the formula of the circumference, which ir:
C = pi*d
Where C is the circumference and d is the diameter of the circle. If we want to know the value of the pi number we just need to divide both sides of the equation above by d:
C/d = pi*d/d
C/d = pi
Thus, we can write pi as the ratio C:d or C/d, which means, how many times the diameter enters on the circumference. In our case is:
pi = 31.4/10 = 3.14
And 3.14 is how we usually use the pi number.
Discounted price before sales tax = 75/100 x (40 + 24 + 18 x 3) = 3/4 x (64 + 54) = 3/4 x 118 = $88.5
Total price inclusive of sales tax = 107/100 x 88.5 = $94.69
