3^x is raising 3 to an unknown number or variable, while x^3 is raising a variable to 3 (x*x*x)
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
Hi pupil here's your answer ::
____________________________
The unit rate depicted in the graph is must be
3 laps in 4 minutes . As we can see in the graph that the point meets at the 3 laps and 4 minutes so this option must be suitable for the above question.
____________________________
hope that it helps. . . . . .
Answer:
Option A is correct.
Step-by-step explanation:
64 < x < 68
This inequality represent that the height x should be greater than 64 and less than 68.i.e.
x>64 and x<68
So, Option A is correct.
The answer is 6. Because 4x6=32
