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:
12 seconds.
Step-by-step explanation:
Let t represent time taken by code to sort an array of 24 elements.
We have been given that an algorithm takes 4 seconds to sort an array of 8 elements. We are asked to find the time it will take for same code to sort an array of 24 elements.
We will use proportions to solve our given problem.





Therefore, it will take 12 seconds for the same code to sort an array of 24 elements.
Answer:
you should subtract x.
Step-by-step explanation:
Let’s do 3x - 8 ≤ 23 first.
You need to rearrange this so that x is on its own.
+8 to both sides
3x ≤ 31
/3 on both sides
x ≤ 31/3
Then the second, -4x + 26 ≥ 6
-26 from both sides
-4x ≥ -20
/-4 on both sides
x ≥ 5
So x is greater than or equal to 5, which can also be written as 5 ≤ x
And for the first one, x is less than or equal to 31/3, which can still be written as x ≤ 31/3, so your final answer is:
5 ≤ x ≤ 31/3