A LOT OF POINTS!!!!!!! PLEASE HELP ME BECAUSE I DONT GET!!! Explain why 9(t - 1) is equivalent to 9t - 9 PLEASE TELL ME THE CORR
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1. As you can tell from the function definition and plot, there's a discontinuity at x = -2. But in the limit from either side of x = -2, f(x) is approaching the value at the empty circle:
Basically, since x is approaching -2, we are talking about values of x such x ≠ 2. Then we can compute the limit by taking the expression from the definition of f(x) using that x ≠ 2.
2. f(x) is continuous at x = -1, so the limit can be computed directly again:
3. Using the same reasoning as in (1), the limit would be the value of f(x) at the empty circle in the graph. So
4. Your answer is correct; the limit doesn't exist because there is a jump discontinuity. f(x) approaches two different values depending on which direction x is approaching 2.
5. It's a bit difficult to see, but it looks like x is approaching 2 from above/from the right, in which case
When x approaches 2 from above, we assume x > 2. And according to the plot, we have f(x) = 0 whenever x > 2.
6. It should be rather clear from the plot that
because sin(x) + 3 is continuous at x = 0. On the other hand, the limit at infinity doesn't exist because sin(x) oscillates between -1 and 1 forever, never landing on a single finite value.
For 7-8, divide through each term by the largest power of x in the expression:
7. Divide through by x². Every remaining rational term will converge to 0.
8. Divide through by x² again:
9. Factorize the numerator and denominator. Then bearing in mind that "x is approaching 6" means x ≠ 6, we can cancel a factor of x - 6:
10. Factorize the numerator and simplify:
where the last equality holds because x is approaching +∞, so we can assume x ≠ -1. Then the limit is
About 92 days are taken for 90 % of the material to <em>decay</em>.
The mass of radioisotopes (), measured in milligrams, decreases exponentially in time (
), measured in days. The model that represents such decrease is described below:
(1)
Where:
- Initial mass, in milligrams.
- Current mass, in milligrams.
- Time constant, in days.
In addition, the time constant is defined in terms of half-life (), in days:
(2)
If we know that ,
and
, then the time required for decaying is:
About 92 days are taken for 90 % of the material to <em>decay</em>.
We kindly invite to check this question on half-life: brainly.com/question/24710827