Answer:
ln(5/3)
Step-by-step explanation:
The desired limit represents the logarithm of an indeterminate form, so L'Hopital's rule could be applied. However, the logarithm can be simplified to a form that is not indeterminate.
<h3>Limit</h3>
We can cancel factors of (x-1), which are what make the expression indeterminate at x=1. Then the limit can be evaluated directly by substituting x=1.
Reorder 2 cos (2y) and sin (2y)
= sin (2y)(2 cos(2y))
Remove parenthesis
= sin (2y) * 2 cos (2y)
Reorder sin (2y) and 2
= 2 * sin (2y) cos (2y)
Apply the sine double-angle identity
= sin (2(2y))
Now multiply 2 by 2
<u>= sin (4y) </u>
Hello,
Please, see the attached files.
Thanks.
Answer:
$1.95
Step-by-step explanation:
notebook = n
pencil = p
3n + 2p = 5.10
2n + 3p = 4.65
multiply top equation by 2 and bottom by 3
6n + 4p = 10.20
6n +9p = 13.95
subtract bottom equation from the top equation
-5p = -3.75
divide by 5, negatives cancel out
p = 0.75
sub p into either equation, I chose the original top equation
3n + 2(0.75) = 5.10
3n + 1.50 = 5.10
subtract 1.50 from both sides
3n = 3.60
divide both sides by 3
n = 1.20
p = 0.75
n + p = 1.95 (the fourth option)
