Looks like the given limit is
With some simple algebra, we can rewrite
then distribute the limit over the product,
The first limit is 0, since 1/3ⁿ is a positive, decreasing sequence. But before claiming the overall limit is also 0, we need to show that the second limit is also finite.
For the second limit, recall the definition of the constant, <em>e</em> :
To make our limit resemble this one more closely, make a substitution; replace 9/(<em>n</em> - 9) with 1/<em>m</em>, so that
From the relation 9<em>m</em> = <em>n</em> - 9, we see that <em>m</em> also approaches infinity as <em>n</em> approaches infinity. So, the second limit is rewritten as
Now we apply some more properties of multiplication and limits:
So, the overall limit is indeed 0:
Answer; $1
Explanation 3 divided by 3
Answer:
Answers may vary but will most likely be close to 2.
Step-by-step explanation
- Given:
first test:38%
second test:76%
SIMULATION FIRST TEST
Randomly select a 2-digit number.
If the digit is between 00 and 35 then you passed the test,else you did not pass the test.
SIMULATION SECOND TEST
Randomly select a 2-digit number.
if the digit is between 00 and 75 then you passed the test,else you did not pass the test.
SIMULATION TRIAL
Perform the simulation of the first test.if you did not pass the first test then perform the simulation of the second test.
Record the number of trials needed to pass the first or second test.
Repeat 20 times and take the average of the 20 recorded number of trials
(what is the sum of recorded values divided by 20).
Note:you will most likely obtain a result of about two trials needed.
