Let p(x) be a polynomial, and suppose that a is any real
number. Prove that
lim x→a p(x) = p(a) .
Solution. Notice that
2(−1)4 − 3(−1)3 − 4(−1)2 − (−1) − 1 = 1 .
So x − (−1) must divide 2x^4 − 3x^3 − 4x^2 − x − 2. Do polynomial
long division to get 2x^4 − 3x^3 − 4x^2 – x – 2 / (x − (−1)) = 2x^3 − 5x^2 + x –
2.
Let ε > 0. Set δ = min{ ε/40 , 1}. Let x be a real number
such that 0 < |x−(−1)| < δ. Then |x + 1| < ε/40 . Also, |x + 1| <
1, so −2 < x < 0. In particular |x| < 2. So
|2x^3 − 5x^2 + x − 2| ≤ |2x^3 | + | − 5x^2 | + |x| + | − 2|
= 2|x|^3 + 5|x|^2 + |x| + 2
< 2(2)^3 + 5(2)^2 + (2) + 2
= 40
Thus, |2x^4 − 3x^3 − 4x^2 − x − 2| = |x + 1| · |2x^3 − 5x^2
+ x − 2| < ε/40 · 40 = ε.
Answer:
total cost = $22.4 + $1.12 = $23.52
Step-by-step explanation:
Mr McNeil bought 2 magazines for $7.45 and 1 book for $14.95 . The sales tax is 6% . The total cost of Mr McNeil can be calculated as follows.
He bought 2 magazines for $7.45 .This means the sum of the prize of the 2 magazine he bought is $7.45 and the prize for the single book he bought is $14.95. The total cost of the items he bought excluding the sales tax is the sum of the whole items he bought.
total cost excluding sales tax = $7.45 + 14.95 = $22.4
The sales tax is 5% which can be calculated as follows
5/100 × 22.4 = 112/100 = $1.12
The total cost of Mr McNeil purchase including his sales tax is
total cost = $22.4 + $1.12 = $23.52
The answer should be 26 hours
That's how many ounces of water you should drink per day. For instance, a person who is 200 pounds, should drink 100 oz. of water per day to be adequately hydrated. (That's 12.5 glasses of water!)
