3) We have
which has vertical asymptotes (i.e. infinite discontinuities) whenever the denominator is zero. This happens for
(where is any integer)
So the graph of has vertical asymptotes whenever and .
4) Given
we have the one-sided limits
and
The one-sided limits don't match, so the two-sided limit does not exist. In other words, the limit does not exist at because the function approaches different values from the left and right side of .
The answer would be B: Dividing the number by 1000
Every time you move the decimal, add a zero. Since the decimal is moved three times, there are three zeroes. When you move left, the number is getting smaller so it is division.
1.5 +.15 = 1.65. 10% x 15 + 1% x 15
Answer:
81mm
Step-by-step explanation:
the number of steps is small enough that we can simply list out each step
let the time elapsed be t and the original length be L ( = 1 mm)
when t = 0, L = 1mm
when t = 10, L = 3mm
when t = 20, L = 3 x 3 = 9mm
when t = 30, L = 9 x 3 = 27mm
when t = 40, L = 27 x 3 = 81mm