Given a function <em>g(x)</em>, its derivative, if it exists, is equal to the limit
The limit is some expression that is itself a function of <em>x</em>. Then the derivative of <em>g(x)</em> at <em>x</em> = 1 is obtained by just plugging <em>x</em> = 1. In other words, find <em>g'(x)</em> - and this can be done with or without taking a limit - then evaluate <em>g'</em> (1).
Alternatively, you can directly find the derivative at a point by computing the limit
But this is essentially the same as the first method, we're just replacing <em>x</em> with 1.
Yet another way is to compute the limit
but this is really the same limit with <em>h</em> = <em>x</em> - 1.
You do not compute <em>g</em> (1) first, because as you say, that's just a constant, so its derivative is zero. But you're not concerned with the derivative of some <em>number</em>, you care about the derivative of a function that depends on a <em>variable.</em>
Answer:
8/22, 16/44, etc
Step-by-step explanation:
.................
Answer:
40 students choose Papa John's, and 24 did not
Step-by-step explanation:
This question can be solved by proportions, using rule of three.
For each 8 students, 5 chose Papa John's. Out of 64, how many choose?
5 - 8
x - 64
Applying cross multiplication
Simplifying by 8
40 students choose Papa John's.
In all, there are 64 students, so 64 - 40 = 24 did not
Answer:
B
C
Step-by-step explanation:
Convert 30% to a decimal:
30% = 0.30
Check each item by multiplying the original price by 0.30 (the 30% off sale). Subtract the product from the original price. If the sale price is the same, the pricing is correct. If they are different, the pricing is incorrect.
Headphones:
24.50 × 0.30
7.35
24.50 - 7.35
17.15
17.15 = 7.35? Incorrect.
Phone Charger:
29.25 × 0.30
8.775
29.25 - 8.775
20.475
Round to the nearest cent (hundredths place):
20.48
20.48 = 20.48? Correct.
Minitablet:
117.95 × 0.30
35.385
117.95 - 35.385
82.565
Round to the nearest cent:
82.57
82.57 = 82.57? Correct.
Printer:
213.45 × 0.30
64.035
213.45 - 64.035
149.415
Round to the nearest cent:
149.416
149.416 = 207.47? Incorrect.
Flat Screen TV:
376.98 × 0.30
113.094
376.98 - 113.094
263.886
Round to the nearest cent:
263.89
263.89 = 236.89? Incorrect.
