Hello,
Use the factoration
a^2 - b^2 = (a - b)(a + b)
Then,
x^2 - 81 = x^2 - 9^2
x^2 - 9^2 = ( x - 9).(x + 9)
Then,
Lim (x^2- 81) /(x+9)
= Lim (x -9)(x+9)/(x+9)
Simplity x + 9
Lim (x -9)
Now replace x = -9
Lim ( -9 -9)
Lim -18 = -18
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The second method without using factorization would be to calculate the limit by the hospital rule.
Lim f(x)/g(x) = lim f(x)'/g(x)'
Where,
f(x)' and g(x)' are the derivates.
Let f(x) = x^2 -81
f(x)' = 2x + 0
f(x)' = 2x
Let g(x) = x +9
g(x)' = 1 + 0
g(x)' = 1
Then the Lim stay:
Lim (x^2 -81)/(x+9) = Lim 2x /1
Now replace x = -9
Lim 2×-9 = Lim -18
= -18
-5 could not be used in the table again, because we have the value of x=-5 for the value of 15. Therefore correct option is C.
Answer: C. -5
Kylie's first month collection, a1= $ 145
Second month collection , a2= $145+ 20
Third month collection, a3 = $145 +2*20
.
.
.
.
so for n months collection = an-1+20
We get an= 20 + an-1 and a1=145
The probability of selecting a yellow marble is #of yellow marbles/total # of marbles= 6/30 or .2 or 20%
If there are 300 marbles in the bag, a good estimate for the total number of red marbles in the bag is 90.
9/30=.3 = the percentage of red marbles
.3(300) = 90
5% of 1000 is 5 * 1000 / 100 = 5000 / 100 = 50.
