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:
I don't have the graph, but I'll explain what you need to do. Plot a point with the coordinates (1,3.5), (2,7), (3,10.5), and (4,14). Now draw a straight line connecting al these pints but don't go past the origin into the negative as in this situation it is not possible. There! Now you have a graph :)
When it comes to hundreds and thousands and even millions, you can tell how much bigger something is by how many more zeros are at the end. Each new zero added, is another rank up. The system goes:
1=10x bigger
2=100x bigger
3=1000x bigger
4=10000x bigger
5=100000 bigger
so on and so forth. There are 2 zeros in 700, and only 1 zero in 70, the difference in zeros is 1, so you can refer to the chart and conclude that 700 is 10 times bigger than 70. You could also divide 700 by 70 to get 10. This is more accurate, but the chart is simpler.
H = 1st row 4 -2 5
2nd row 6 1 -3
J = 1st column 7 3 8
1st row and 1st column: 4*7 + -2*3 + 5*8 = 28 - 6 + 40 = 62
2nd row and 1st column: 6*7 + 1*3 + -3*8 = 42 + 3 - 24 = 21
Answer is 2nd option. 62 and 21.
