Insight number 2: to evaluate the limit of a: 1. Rational function: you can factorize and cancel out what you can
2. Radicals (subtractions of square roots): multiply and divide by the
conjugate. For example:
√x² +1-x
x² + 1 - x²
x2 + 1 - x=
(V x2 +1+
+x)
Vx2 + 1 + x
Vx2 + 1 + x
1
VX2 + 1 + x
3. Trigonometric functions: try to connect your limit with important
trigonometric limits like limx-
= 1
If you are stuck with a trig limit, express all the trig functions in terms
of sine and cosine.
4. If you are composing continuous functions, you can pass the limit
inside the external function: limz-a f(g(x)) = f(limz-a 9(x))
sin (x)

70 years.

step-by-step explanation:

the above table 1 will calculate the population size (n) after a certain length of time (t). all you need to do is plug in the initial population number (no), the growth rate (r) and the length of time (t). the constant (e) is already entered into the equation. it stands for the base of the natural logarithms (approximately 2.71828). growth rate (r) and time (t) must be expressed in the same unit of time, such as years, days, hours or minutes. for humans, population growth rate is based on one year. if a population of people grew from 1000 to 1040 in one year, then the percent increase or annual growth rate is 40/1000 x 100 = 4 percent.

step-by-step explanation: