When we approach limits, we are finding values that are infinitesimally approaching this x-value. Essentially, we consider the approximate location that this root or limit appears. This is essential when it comes to taking Calculus, and finding the limit or rate of change of a function.
When we are attempting limits questions, there are several tests we attempt first.
1. Evaluate the limit by substituting the value of the x-value as it approaches the value (direct evaluation of a limit)
2. Rearrangement of the function, such that we can evaluate the limit.
3. (TRIGONOMETRIC PROPERTIES)


4. Using L'Hopital's Rule for indeterminate limits, such as 0/0, -infinity/infinity, or infinity/infinity.
For example:
1)

We can do this using the first and second method.
<em>Method 1: Direct evaluation:</em>Substitute x = 0 to the function.


<em>Method 2: Rearranging the function
</em>We can see that x - 25 can be rewritten as: (√x - 5)(√x + 5)
By rewriting it in this form, the top will cancel with the bottom easily, and our limit comes out the same.



Every example works exactly the same way, and by remembering these criteria, every limit question should come out pretty naturally.
Answer:
0.150,0.595
Step-by-step explanation:
Given that at a self-service gas station, 40% of customers pump regular gas, 35% pump midgrade, and 25% pump premium gas. Of those who pump regular, 30% pay at least $30. Of those who pump midgrade, 50% pay at least $30. And of those who pump premium, 60% pay at least $30.
Regular gas Midgrade Premium gas Total
Percent 40 35 25 100
atleast 30 30% 50% 60%
a) The probability that the next customer pumps premium gas and pays at least $30
=
b) the probability that the next customer pays at least $30
= P(regular and pays atleast 30%)+P(premium and pays atleast 30%)+P(midgrade and pays atleast 30%)
=
Answer:
9/a
Step-by-step explanation:
8/a - 6/a + 7/a
Since the denominators are the same, we can add the numerators
8-6+7 =9
Then put it over the common denominator a
9/a
2 and 1/2 years = 30 months



The answer is A. $150
Hope this helps.
Answer:
1
Step-by-step explanation: