The solution is (3,2) cause both of the lines intersect at one point (which is a solution),and that point is (3,2) :)
Answer:
-x¹⁴ / 5040
-½ < x < ½
Step-by-step explanation:
f(x) = e^(-x²)
The Taylor series for eˣ centered at 0 is:
eˣ = ∑ (1/n!) xⁿ
Substitute -x²:
e^(-x²) = ∑ (1/n!) (-x²)ⁿ
e^(-x²) = ∑ (1/n!) (-1)ⁿ x²ⁿ
The 14th degree term occurs at n=7.
(1/7!) (-1)⁷ x¹⁴
-x¹⁴ / 5040
ln(1 + x) = ∑ₙ₌₁°° (-1)ⁿ⁺¹ xⁿ / n
If we substitute 4x²:
ln(1 + 4x²) = ∑ₙ₌₁°° (-1)ⁿ⁺¹ (4x²)ⁿ / n
Using ratio test:
lim(n→∞)│aₙ₊₁ / aₙ│< 1
lim(n→∞)│[(-1)ⁿ⁺² (4x²)ⁿ⁺¹ / (n+1)] / [(-1)ⁿ⁺¹ (4x²)ⁿ / n]│< 1
lim(n→∞)│-1 (4x²) n / (n+1)│< 1
4x² < 1
x² < ¼
-½ < x < ½
To make this easy let covert everything using a LCD.
The LCD of 1/4 1/12 and 1/6 is 12. This becomes...
Tom ate 3/12 of the pizza.
Leftover pizza = 9/12.
Slices were 1/12.
X friends got pizza.
Remaining pizza is 2/12.
if each friend got 1 piece(1/12)....
9/12(Leftovers) - 2/12(remaining) = 7/12
So 7 friends got pizza.
@Texaschic101 you are correct .75 x 64 will indeed equal 48 sq feet. so your answer will be 64 tiles. hope this was of help!
