2(2x+1)= (2 x 2x) + (2 x 1) = 4x + 2
(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.
Step-by-step explanation:
a) The circumference of a circle is 360 degrees. so:
7x+15+8x+6x+30=360
21x+45=315
21x=135
x=<u>15</u>
b) This means 7(15)+15=120, 8(15)=120, and 6(15)+30=120. Thus, by the inscribed angle theorem, all the angles measure 60 degrees, and the triangle is thus <u>equilateral</u> and <u>isosceles</u>.
Answer:
The geometric mean of 6 and 30 is 13.416407864999
Y - 4 = 6 (x - 7) is the correct equation
