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
Answer:
I dont know what options you have but all these are possible answers
y - 5 = 1/2 ( x - 4 )
y - 3 = 1/2 x
y = 1/2 x + 3
Step-by-step explanation:
In order to find the equation you need a slope, so you find the slope of both points by using the slope equstion
y2 - y1 / x2 - x1
and you would get :
now you plug it into the point slope formula which is y - y = m ( x - x )
and you choose one of the two sets of points that they provided in the question but you'll get the same answer either way.
Answer:
Alternate Interior Angles:
∠3 ≅ ∠5
Corresponding Angles:
∠3 ≅ ∠7
∠4 ≅ ∠8
Supplementary Angles:
∠3 is supplementary to ∠6
Step-by-step explanation:
Answer:
n = 1
Step-by-step explanation:
Represent the number by n. Then "seven less than twice a number is -5 becomes 2n - 7 = -5
Next we must solve for n. Adding 7 to both sides yields 2n = 2, so that
n = 1