The graph of a function is given. Use the graph to find the indicated limit and function value, or state that the limit or function value does not exist.
a. limx→3 f(x)
b. f(3)
(EQUATION AND ANSWER CHOICES BELOW)
Answers
Answer:
The fourth one down
Step-by-step explanation:
In order for the limit of a function to exist, the general limit that is, it has to agree from both the left and the right of the function. Since this is not asking for a left-handed limit or a right-handed limit, coming in from both the left and right does not equal the same y value. So the limit does not exist.
To find f(3), look to where x = 3 and find the y value where the solid dot at x=3 is. When x = 3, the solid dot has a y value of 5. Therefore, f(3) = 5.
The answer you want is the fourth one down.
The limit of function at x = 3 doest not exist and value of function will be f(3) = 5 so option (D) will be correct.
What is limit?Limit, a nearness in mathematical notion, is largely used to give values to some functions at locations that were usually not given or defined, in a manner consistent with neighboring values.
In another word, limit is a mathematical concept in which we find out the value of any function at a point by its adjacent very close point.
Because the value of that function at that point doesn't define.
Given a function f(x)
As we can see that the function is breaking at x = 3 into two functions.
To exist any limit the left-hand limit must be equal to the right-hand limit
Left-hand limit
LHL = 3
Right-hand limit
RHL = 5
Since limits are not equal hence limits do not exist.
Now value of functon f(x) at x = 3 is 5 not 3 becuase at 3 the point is hollow while at x = 5 point is solid.
Hence,the limit of function at x = 3 doest not exist and value of function will be f(3) = 5
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Related Questions
Find the value of x.
10
11
14
9
Answers
The mid line of a triangle is always half of the triangle's "base"
Plug all the answer choices in and see if they produce a true answer
20 = (2(10) - 8) * 2
20 = (20 - 8) * 2
20 = 12 * 2
20 ≠ 24
10 is NOT x
20 = (2(11) - 8) * 2
20 = (22 - 8) * 2
20 = 14 * 2
20 ≠ 28
11 is NOT x
20 = (2(14) - 8) * 2
20 = (28 - 8) * 2
20 = 20 * 2
20 ≠ 40
14 is NOT x
20 = (2(9) - 8) * 2
20 = (18 - 8) * 2
20 = 10 * 2
20 = 20
9 IS x!!!
Or you can do it this way:
20 = (2x - 8) * 2
Divide 2 to both sides
10 = 2x - 8
18 = 2x
x = 9
Hope this helped!
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Break downs occur on a 20-years-old car with rate λ= 0.5 breakdowns/week. The owner of the car is planning to have a trip on his car for 2 weeks. What is the probability that there will be no breakdown on his car in the trip?
Answers
Answer: There is probability of 0.367 that there will be no breakdown on his car in the trip.
Step-by-step explanation:
Since we have given that
Mean (λ) = 0.5 breakdown per week
Number of weeks the owner of the car is planning to have a trip on his car for = 2 weeks
So, mean for 2 weeks would be
[tex]0.5\times 2=1.0[/tex]
We need to find the probability that there will be no breakdown on his car in the trip.
Probability that there will be no breakdown on his car in the trip is given by
P(X=0) is given by
[tex]\dfrac{e^{-\lambda}\lambda^k}{k!}\\\\=\dfrac{e^{-1}1^0}{0!}\\\\=0.367[/tex]
Hence, there is probability of 0.367 that there will be no breakdown on his car in the trip.
The average value of a function f(x, y, z) over a solid region E is defined to be fave = 1 V(E) E f(x, y, z) dV where V(E) is the volume of E. For instance, if ρ is a density function, then ρave is the average density of E. Find the average value of the function f(x, y, z) = 3x2z + 3y2z over the region enclosed by the paraboloid z = 9 − x2 − y2 and the plane z = 0.
Answers
The volume of [tex]E[/tex] is
[tex]\displaystyle V(E)=\iiint_E\mathrm dV[/tex]
To compute the integral, convert to cylindrical coordinates:
[tex]x=r\cos\theta[/tex]
[tex]y=r\sin\theta[/tex]
[tex]z=z[/tex]
[tex]\implies\mathrm dV=r\,\mathrm dr\,\mathrm d\theta\,\mathrm dz[/tex]
[tex]\displaystyle V(E)=\int_0^{2\pi}\int_0^3\int_0^{9-r^2}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta=\frac{81\pi}2[/tex]
Now integrate [tex]f[/tex] over [tex]E[/tex]. In cylindrical coordinates, we get
[tex]\displaystyle\iiint_E3x^2z+3y^2z\,\mathrm dV=3\int_0^{2\pi}\int_0^3\int_0^{9-r^2}r^3z\,\mathrm dz\,\mathrm dr\,\mathrm d\theta=\frac{6561\pi}8[/tex]
Then the average value of [tex]f[/tex] over [tex]E[/tex] is [tex]\dfrac{\frac{6561\pi}8}{\frac{81\pi}2}=\dfrac{81}4[/tex].
The average value of a function over a certain region can be found by integrating the function over the volume and then dividing by the volume. For the given function and region, one would integrate over the range of values that satisfy the inequality z = 9 - [tex]x^2 - y^2[/tex] >= 0.
Explanation:The average value of the function f(x, y, z) = [tex]3x^2z + 3y^2z[/tex] over the region enclosed by the paraboloid z = 9 −[tex]x^2 - y^2[/tex] and the plane z = 0 can be calculated by integrating the function over the volume and then dividing by the volume. This is somewhat analogous to how one would calculate an average in a discrete distribution.
The volume V(E) of the region E enclosed by the paraboloid and the plane can be found by integrating the equation of the paraboloid over the range of x and y values that satisfy the inequality z = 9 - [tex]x^2 - y^2[/tex] ≥ 0. After finding V(E), you then integrate the function f(x, y, z) over the same range of x, y, and z values to find the total of f over the volume. The average value is then the total divided by V(E).
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Saif is putting tiles on a concrete bird bath. The bird bath is in the shape of a cube with one open face. It takes 4 tiles to cover one square foot of area. Explain how to use a net to find the number of tiles you need to cover the entire outer surface of the bird bath.
Answers
Answer: The net is made of 6 squares, but one face is open. I would add the area of 5 squares to get the surface area in square feet. Then, I would multiply the area by 4 to find the number of tiles needed to cover the surface area.
Step-by-step explanation:
How to use a net to find the number of tiles needed to cover the entire outer surface of the bird bath is: Multiply the surface area by 4.
What is Surface area?Surface area can be defined as the number of space that cover the outer surface of a dimensional shape.
Since 4 cover one square foot of area in order to determine the number of tiles to cover the outer surface let the net be 6 squares and the surface area be 5 squares because we have one open face.
Multiply the surface area by the 4 tiles which will give us the number of tiles needed.
Therefore Multiply the surface area by 4.
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