(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:
Step-by-step explanation:
one hour makes 3.75
20*3.75 = 75
Answer:
the first one is triangle and the second one is rectangle
Step-by-step explanation:
i just did it on edge
Answer:
l=10 cm
Step-by-step explanation:
In a rhombus, the diagonals are cut into identical lines at the intersection.
This way, I found the measures of the halves of the diagonals in a right triangle, knowing that the diagonals of the rhombus are perpendicular on each other.
I calculated that AO = AC/2= 8, and that BO=BD/2= 6, and then I applied pytagora's theorem in a quarter of the rhombus, which is the right triangle AOB, to find the length of a side
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