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Discuss whether R is continuous at c.Use limits to analyze the graph of R at c. Graph R.

0 votes

Discuss whether R is continuous at c.Use limits to analyze the graph of R at c. Graph R.

asked Feb 16, 2015 in PRECALCULUS by anonymous

1 Answer

0 votes

Step 1:

The function is , and .

The domain of a function is all values of , those makes the function mathematically correct.

The denominator of the function should not be zero.

image

image

image

The domain of function is all real numbers except image and image.

The domain of function is image.

Step 2:

Rewrite the function as image.

Cancel common terms.

image.

The removable discontinuity is at image.

is in the domain and is not in the domain.

The function is continuous every number on its domain.

Find the limit at is .

.

The hole is at image.

answered Feb 24, 2015 by Sammi Mentor
edited Feb 24, 2015 by Sammi

Contd...

Step 3:

Graph the function:

image

Observe the graph:

As  tends to 1 from the left hand side the limit approaches to .

image

As  tends to 1 from the right hand side the limit approaches to .

image

The vertical asymptote at image.

The hole at image.

Solution:

image.

image.

image.

The hole at image.

The vertical asymptote at image.

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