Eilb0e4niMorty Eilb0e4niMorty

06-08-2016
Mathematics

Answered

Show by means of an example that lim x-> a [f(x) + g(x)] may exist even though neither lim x-> a f(x) and lim x -> a g(x) exists.

Verified Answer :

meerkat18 meerkat18

11-08-2016

To evaluate the limit, we substitute zero to function 1/x resulting to infinity. Hence,
limit from left = -∞
limit from right = ∞
Thus,
f(x) g(x) = (1/x) (1/x) = 1/x²

as x ->0:
lim from left = ∞
lim from right = ∞
lim = ∞

Limit thus doesn't exist

Answer Link

Related Questions

As a result of the Persian Wars of the 5th century BC a Athens took the lead in organizing an alliance of Greek citystates against further attacks by the Persia

Should Spanish Colonial settlers accept the new laws of 1542

which algebraic expression is equivalent to the expression below9x 10 10

is times and divide the same explain

When a landslide occurs it is most like due to ASoil creep BSlumping CRock metamorphosis DHigh winds

what are even numbers

Next17End of Semester Test English 11BSelect the correct answerIn hard scifi how is the bombing of Hiroshima and Nagasaki viewedOA000a destructive eventB a joyo

Is knowing the abo blood type of a potential donor enough to determine a suitable match

What group did the colonies organize to fight against Great Britain

How many chambers does the heart contain A 3 B 4 C 5 D 6

Web Analytics