Answer:
6
Step-by-step explanation:
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:
5.5 inches
Step-by-step explanation:
Since it is a hexagon, there is 6 faces. The total lateral area is 6 times area of one face. The area of one face is 12 times the width so the total is 6*12*width which equals 396. Dividing both sides by 6 gives you 12*width = 66. Dividing both sides by 12 gives you width = 5.5.
Answer:
x=2
y=3
Step-by-step explanation:
x/2+y/3=2 so
3x/6+2y/6=12/6
then multiply by 6
<em>3x+2y=12</em>
equation number 2
x/3+y/2=13/6
2x/6+3y/6=13/6
multiply by 6
<em>2x+3y=13</em>
so the system is now
<em>3x+2y=12</em>
<em>2x+3y=13</em>
<em>from the first equation 2y=12-3x, y=6 - 3x/2</em>
<em>then put y in the second equation</em>
<em>2x+3*(6-3x/2)=13</em>
<em>2x+18-9x/2=13</em>
<em>2x-9x/2=13-18</em>
<em>4x/2-9x/2=-5</em>
<em>-5x/2=-5</em>
<em>*(-1/5) *(-1/5)</em>
<em>x/2=1</em>
<em>*2 *2</em>
<em>x=2</em>
<em>so y=6-3*2/2=6-3</em>
<em>y=3</em>
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2/5 of the students or two fifths
