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joejoefofana
19.07.2019 •
Mathematics
Given that lim x→a f(x) = 0 lim x→a g(x) = 0 lim x→a h(x) = 1 lim x→a p(x) = ∞ lim x→a q(x) = ∞, evaluate the limits below where possible. (if a limit is indeterminate, enter indeterminate.) (a) lim x→a [f(x) − p(x)] (b) lim x→a [p(x) − q(x)] (c) lim x→a [p(x) + q(x)]
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Ответ:
Using limit properties, it is found that:
a)![\lim_{x \rightarrow a} [f(x) - p(x)] = -\infty](/tpl/images/0109/0640/f8038.png)
b) Undetermined.
c)![\lim_{x \rightarrow a} [p(x) + q(x)] = \infty](/tpl/images/0109/0640/a957f.png)
In this problem, the property considered is:
The limits of the sum/subtraction is the sum/subtraction of the limits.Item a:
Item b:
Then undetermined.
Item c:
A similar problem is given at link
Ответ:
(a)![L=-\infty](/tpl/images/0109/0640/a3e54.png)
(b)![L=\text{Indeterminate}](/tpl/images/0109/0640/7ffc8.png)
(c)![L=\infty](/tpl/images/0109/0640/71d7e.png)
Step-by-step explanation:
We are given,
Evaluate the limit:
(a)![L=\lim_{x\rightarrow a}[f(x)-p(x)]](/tpl/images/0109/0640/f8d1a.png)
Using limit property, Distribute the limit
(b)![L=\lim_{x\rightarrow a}[p(x)-q(x)]](/tpl/images/0109/0640/a5b39.png)
Using limit property, Distribute the limit
Because difference of two infinity might be finite or infinite.
(c)![L=\lim_{x\rightarrow a}[p(x)+q(x)]](/tpl/images/0109/0640/af4b0.png)
Using limit property, Distribute the limit
Ответ:
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