Use the given graph to determine the limit, if it exists.

Asked by maham237 @ 23/12/2020 in Mathematics viewed by 302 People

Use the given graph to determine the limit, if it exists. A coordinate graph is shown with a horizontal line crossing the y axis at six that ends at the open point 2, 6, a closed point at 2, 1, and another horizontal line starting at the open point 2, negative 3. Find limit as x approaches two from the left of f of x. and limit as x approaches two from the right of f of x..

Answered by maham237 @ 23/12/2020

Answer:

The limit of the function does not exists.

Step-by-step explanation:

From the graph it is noticed that the value of the function is 6 from all values of x which are less than 2. At x=2, the line y=6 has open circle. It means x=2 is not included.

For x<2

$f(x)=6$

The value of the function is -3 from all values of x which are greater than 2. At x=2, the line y=-3 has open circle. It means x=2 is not included.

For x>2

$f(x)=-3$

The value of y is 1 at x=2, because of he close circles on (2,1).

For x=2

$f(x)=1$

Therefore the graph represents a piecewise function, which is defined as

$f(x)=\begin{cases}6& \text{ if } x2 \end{cases}$

The limit of a function exist at a point a if the left hand limit and right hand limit are equal.

$lim_{x\rightarrow a^-}f(x)=lim_{x\rightarrow a^+}f(x)$

The function is broken at x=2, therefore we have to find the left and right hand limit at x=2.

$lim_{x\rightarrow 2^-}f(x)=6$

$lim_{x\rightarrow 2^+}f(x)=-3$

$6\neq-3$

Since the left hand limit and right hand limit are not equal therefore the limit of the function does not exists.

One manufacturer boxes screws so that each box weighs the same no matter what size the screws are. the graph shows the amount of allowed weight remaining in a given shipment depending on the number of boxes of screws already included

Asked by maham237 @ 13/01/2021 in Mathematics viewed by 370 persons

Use the given graph to determine the limit, if it exists.

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