Answer:
-3(3+4x)
Step-by-step explanation:
Answer:
0 ≤ an ≤ bn
The series ∑₁°° bn converges
The series ∑₁°° an converges by comparison to ∑₁°° bn.
0 ≤ an ≤ bn
The series ∑₁°° bn diverges
The comparison test is inconclusive for our choice of bn.
Step-by-step explanation:
an = 1 / (n² + n + 3) and bn = 1 / n²
The numerators are the same, and the denominator of an is greater than the denominator of bn. So 0 ≤ an ≤ bn.
bn is a p series with p > 1, so it converges.
Since the larger function converges, the smaller function also converges.
an = (3n − 1) / (6n² + 2n + 1) and bn = 1 / (2n)
If we rewrite bn as bn = (3n − 1) / (6n² − 2n), we can tell that when the numerators are equal, the denominator of an is greater than the denominator of bn. So 0 ≤ an ≤ bn.
bn is a p series with p = 1, so it diverges.
The larger function diverges. We cannot conclude whether the smaller function converges or diverges.
Answer:
f(x) = 2(x - 5)² - 6
Step-by-step explanation:
Vertex Formula: <em>y</em><em> </em><em>=</em><em> </em><em>a</em><em>(</em><em>x</em><em> </em><em>-</em><em> </em><em>h</em><em>)</em><em> </em><em>+</em><em> </em><em>k</em>; Vertex: [<em>h</em><em>,</em><em> </em><em>k</em>]; there is a vertical stretch at <em>2</em><em> </em><em>=</em><em> </em><em>a</em><em>.</em><em> </em>The <em>-</em><em>h</em><em> </em>[phase shift (horizontal shift)] in parentheses gives you the OPPOSITE term of what it really is, so really, <em>5</em><em> </em><em>=</em><em> </em><em>h</em><em>.</em><em> </em>Now, <em>k</em><em> </em>[vertical shift] is the ONLY normal term, so <em>-</em><em>6</em><em> </em><em>=</em><em> </em><em>k.</em><em> </em>