Explain what it means to say that lim x → 1 − f ( x ) = 3 and lim x → 1 − f ( x ) = 7 In this situation is it possible that lim x → 1 f ( x ) exists? Explain.
Explain what it means to say that lim x → 1 − f ( x ) = 3 and lim x → 1 − f ( x ) = 7 In this situation is it possible that lim x → 1 f ( x ) exists? Explain.
Figure out that this statement is true or false? if is false explain why? by using example, and if it is true explain why?
When lim x → a f ( x ) exists, the limit is always equal to f ( a ) - Is this statement true or false?
determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.
If
lim x→7 g(x) = 0
and
lim x→7 f(x)/g(x) = 0
exists, then
lim x→7 f(x) = 0.
True. If lim x→7 f(x) is not equal to zero and lim x→7 g(x) = 0, then lim x→7 f(x)/g(x) does not exist.
True. Any number divided by zero is equal to zero.
False. Let g(x) = (x − 7) and f(x) = (x − 1)(x − 7). Then lim x→7 g(x) = 0 and lim x→7 f(x)/g(x) = 0 exists, but lim x→7 f(x) is not equal to 0.
False. Divison by zero is not allowed.
False. There is not enough information given to determine lim x→7 f(x)/g(x)
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