Answer:
A≈1135.93
Step-by-step explanation:
Hope I help
L=Lim tan(x)^2/x x->0
Since both numerator and denominator evaluate to zero, we could apply l'Hôpital rule by taking derivatives.
d(tan^2(x))/dx=2tan(x).d(tan(x))/dx = 2tan(x)sec^2(x)
d(x)/dx = 1
=>
L=2tan(x)sec^2(x)/1 x->0
= (2(0)/1^2)/1
=0/1
=0
Another way using series,
We know that tan(x) = x+x^3/3+2x^5/15+.....
then tan^2(x), using binomial expansion gives
x^2+2*x^4/3+.... (we only need two terms)
and again apply l'Hôpital's rule, we have
L=d(x^2+2x^4/3+...)/d(x) = (2x+8x^3/3+...)/1
=0 as x->0
Answer:
The explicit rule for the arithmetic sequence is given by:
......[1]
where,
is the first term
n is the number of terms and
d is the common difference for two consecutive terms.
As per the statement:
A recursive rule for an arithmetic sequence is:


The recursive formula for the arithmetic sequence is given by:

then;
On comparing we get;
d = -3
Substitute the given values in [1] we have;

⇒
Therefore, the explicit rule for this sequence is, 
Answer:
$0.21
Step-by-step explanation:
So, first let's find the cost of a single cup.
16/13.60 = 1/0.85
Now, we know that each cup is approximately $0.85. Next, we must convert cups into quarts. 1 cup = 0.25 quarts.
1/0.85 = 0.25/0.21
Answer is 56 because on his 3rd exam he got 57 word per minute, since he got 57 he can take out 7 of those words and he would still have 50. Remember the extra 7 words we have. Then you would calculate how many more words he needs to get to fifty on his other exams which are 4,6,and 3. Add these 3 and you get 13. Remember we still have that extra 7. We pick 56 with the extra 7 it would be 63. You can take out 13 words to fill in the other exams and u would still be left with 50.
Therefor your answer is 56.