(a) converges; consider the function <em>f(x)</em> = <em>a</em> ˣ, which converges to 0 as <em>x</em> gets large for |<em>a</em> | < 1. Then the limit is 2.
(b) converges; we have
4ⁿ / (1 + 9ⁿ) = (4ⁿ/9ⁿ) / (1/9ⁿ + 9ⁿ/9ⁿ) = (4/9)ⁿ × 1/(1/9ⁿ + 1)
As <em>n</em> gets large, the exponential terms vanish; both (4/9)ⁿ → 0 and 1/9ⁿ → 0, so the limit is 1.
(c) converges; we know ln(<em>n</em> ) → ∞ and arctan(<em>n</em> ) → <em>π</em>/2 as <em>n</em> → ∞. So the limit is <em>π</em>/2.
Answer:
137°
Explanation:
In any triangle, the measure of the exterior angle is equal to the summation of the measures of the other two non-adjacent angles.
In the given triangle:
Angle 1 is an exterior angle.
The measures of the non-adjacent angles are 103° and 34°
Based on the above theorem:
measure angle 1 = 103 + 34 = 137°
Hope this helps :)
The answer is the second option: T<span>wo places left.
Therefore, the complete text is: "</span>To obtain the number of centimeters from a distance measured in meters, move the decimal point Two places left ".
<span>
The explanation is:
1 meter has 100 centimeters, then, if you have a distance of 45.55 centimeters and you want to know this value in meters, you need to divide it by 100 or, in others words, you need to </span>move the decimal point two places left:
<span>
=(45.55 centimeters)(1 meter/100 centimeters)
=(45.55x1)/100
=0.4555 meters
</span>
First you need to combine like terms
13x+8-15x=6+x+11
-2x+8=x+17
-x -8 -x -8
-3x=9
--- ----
-3 -3
x=-3
I hope I've helped!
Without any calculations it's evident it can't be neither B (both numbers are even, so they're divisible by 2) nor C (the numbers end in 0 and 5, so they're divisible by 5).
A.
Both numbers have a factor of 3, so they're not relatively prime.
That means it must be D. But, let's check it.
Indeed, those two numbers are relatively prime.
