Determine lim_x rightarrow infinity f(x)/g(x) for the conditions (a) through (c)
ID: 2865593 • Letter: D
Question
Determine lim_x rightarrow infinity f(x)/g(x) for the conditions (a) through (c) below. a. If f(x) rightarrow 500,000 and g(x) rightarrow infinity as x rightarrow infinity. Choose the correct answer below. A. lim_x rightarrow infinity f(x)/g(x) = 500,000 B. lim_x rightarrow infinity f(x)/g(x) = 0 C. lim_x rightarrow infinity f(x)/g(x) = 1/500,000 D. lim_x rightarrow infinity f(x)/g(x) = infinity b. If f(x) rightarrow infinity and g(x) rightarrow 500,000 as x rightarrow infinity. Choose the correct answer below. A. lim_x rightarrow infinity f(x)/g(x) = 0. B. lim_x rightarrow infinity f(x)/g(x) = 1/500,000 C. lim_x rightarrow infinity f(x)/g(x) = 500,000 D. lim_x rightarrow infinity f(x)/g(x) = infinity If f(x) rightarrow 500,000 and g(x) rightarrow 0 as x rightarrow infinity. Choose the correct answer below. A. lim_x rightarrow infinity f(x)/g(x)= 1/500,000 B. lim_x rightarrow infinity f(x)/g(x) = plusminus infinity (If the limit exists)Explanation / Answer
Some basic rules.
When the numerator is a finite number and the denominator is infinite then the fraction is very close to 0.
When the numerator is infinite and the denominator is finite then the fraction has a very high(infinite) magnitude.
For all other cases we will observe by case it comes.
a.
In this case the numerator has a finite value and the denominator is going for a very high value. As a result the fraction will go very closer to 0.
Hence option B. is correct.
b.
In this case the numerator is infinite and the denominator is a finite number and hence the fraction will go to a very high value (infinity).
Therefore option D is correct.
c.
In this case since the denominator is assuming a very small value , the whole fraction will take a very high value but depending upon from which side the denominator is approaching 0 the fraction can be positive or negative.
Hence the option C is correct.
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