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: (-2, 2) and (4, 8)
There are two solutions because the two functions cross each other twice.
Answer:
y=2X+9
Step-by-step explanation:
y-7=2(x+1)
Distribute 2 through: y-7=2x+2
Add 7 over to the other side: y=2x+9
Answer:
Correct answer: sa · sb = 2/3 · (- 3/2) = - 1
Step-by-step explanation:
Given:
line A - (x₁, y₁) = (3, -4) and (x₂, y₂) = (6, -2)
line B - (x₁, y₁) = (-1, 5) and (x₂, y₂) = (1, 2)
The slope is calculated using the following formula:
s = (y₂ - y₁) / (x₂ - x₁)
sa = (-2 - (-4)) / (6 - 3) = (-2 + 4) / 3 = 2 / 3
sa = 2 / 3
sb = (2 - 5) / (1 - (-1)) = -3 / 2
when lines are perpendicular to each other then the slopes are in the next relationship:
sa · sb = - 1
we will check:
sa · sb = 2/3 · (- 3/2) = - 1
God is with you!!!
(y-4) (y-3)
you look at 12 and see what two factors of 12 add up to -7 and -4 times -3 is 12 and -4+-3 = -7
