Find lim x->2 for f(x)=
1 answer:
LHL in not equal to RHL , Therefore the limit does not exists , Option D is the answer.(none)
<h3>What is the limit of a function ?</h3>The limit of a function at a certain point is the value that the function approaches as the argument of the function approaches the same point.
It is given that
lim x->2 for f(x)
f(x) = 2x+1 x ≤2
f(x)= x² , x >2
When both the function tends to 2
Left Hand Limit
f(x) = 2 *2 +1
f(x) = 5
Right Hand Limit
f(x) = x² ,
f(x) = 4
LHL in not equal to RHL , Therefore the limit does not exists.
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Answer:
1) The area of the regular hexagon is approximately 11.256 unit²
2) The coordinates of the center is (2, 3)
3) The base length is approximately 2.08 units
4) The height of the hexagon is approximately 3.61 units
Step-by-step explanation:
1) The length, lₐ, of the apothem is given as follows;
Therefore, for the apothem having coordinates, (2, 3), and (3, 1.5), we have;
The length of half half of one side, S/2 = a × tan(30°) = √(3.25)/√3
The length of the base = 2 × √(3.25)/√3 ≈ 2.082 units
The perimeter, P = 6 × 2× √(3.25)/√3
The area, A = 1/2 × P × a = 1/2 × 6 × 2 × √(3.25)/√3 × √3.25 = (13·√3)/2
A = (13·√3)/2 unit²
The area of the regular hexagon, A = (13·√3)/2 unit² ≈ 11.256 unit²
2) The coordinates of the center = (2, 3)
3) The base, 'b', length by Pythagorean theorem is given as follows;
b = √(a² + (S/2)²) = √((√(3.25))² + (√(3.25)/√3)²) = √(3.25 + 3.25/3) = √(13/3) = (√39)/3
The base length, b = (√39)/3 units ≈ 2.08 units
4) The height of the hexagon, h = 2 × The length of the apothem, lₐ
The length, lₐ, of the apothem is given as follows;
Given the apothem coordinates, (2, 3), and (3, 1.5), we have;
The height of the hexagon, h = 2 × √3.25 units ≈ 3.61 units.
I'm not quite sure what you mean by common core way but the way to get the answer the question is this:
1.) You must covert the whole numbers into fractions.
(multiply the denominator by the whole number, which in this case is 4, then add the answer to the numerator).
(same steps will apply as before except in this case there is a different denominator and numerator).
There is no need to make the denominators the same number since it is multiplication and not addition or subtraction (the same can be done with division expect there is one crucial difference which I can explain if you want, in the comments).
2.) Next set up the equation to multiply:
5 and simplify (also note that the only way you can't simplify is across)
3.) Now multiply across:
NUMERATOR
21 × 7 = 147
DENOMINATOR
5 × 8 = 40
It will come together to be 147/40 or 3 27/40
1.) You must covert the whole numbers into fractions.
(multiply the denominator by the whole number, which in this case is 4, then add the answer to the numerator).
(same steps will apply as before except in this case there is a different denominator and numerator).
There is no need to make the denominators the same number since it is multiplication and not addition or subtraction (the same can be done with division expect there is one crucial difference which I can explain if you want, in the comments).
2.) Next set up the equation to multiply:
5 and simplify (also note that the only way you can't simplify is across)
3.) Now multiply across:
NUMERATOR
21 × 7 = 147
DENOMINATOR
5 × 8 = 40
It will come together to be 147/40 or 3 27/40