A 30 ft ladder leans against the side of a house. If the base of the ladder sits 10 ft away from the base of the house, what is
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Answer:
The function is continuous at x = 36.
Step-by-step explanation:
We need to follow the following steps:
The function is:
The function is continuous at point x=36 if:
- The function
exists at x=36.
- The limit on both sides of 36 exists.
- The value of the function at x=36 is the same as the value of the limit of the function at x = 36.
Therefore:
The value of the function at x = 36 is:
The limit of the is the same at both sides of x=36, that is, the evaluation of the limit for values coming below x = 36, or 33, 34, 35.5, 35.9, 35.99999 is the same that the limit for values coming above x = 36, or 38, 37, 36.5, 36.1, 36.01, 36.001, 36.0001, etc.
For this case:
Since
And
Then, the function is continuous at x = 36.