(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:
x=0.5
Step-by-step explanation:
32x+16=32
-16 -16
32x=16
÷32 ÷32
x=0.5 or x=1/2
They are most likely to meet on the 24th since it is a common multiple of both 8 and 3.
Answer:
15 days
Step-by-step explanation:
You'd divide 40 by 2 2/3, getting you 15.Therefore there will be enough food for the dog to eat for 15 days.
Answer:
91
Step-by-step explanation:-5, 1, 7, 13
the common diference is : d = ( 13)-(7)=(7)-(1)=(1)-(-5)=6
the firt term is A1 = -5
the n-ieme term is : An = A1 +(n-1)d
An = -5+6(n-1)
An = 6n-11
the 17th term in the arithmetic sequence is : A17 = 6(17)-11 =91
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