Limit Laws

Question 1

lim [f(x) + g(x)]

Answer 1

lim f(x) + lim g(x)

Question 2

lim [f(x) - g(x)]

Answer 2

lim f(x) - lim g(x)

Question 3

lim c(fx)

Answer 3

c * lim f(x)

Question 4

lim [f(x) * g(x)]

Answer 4

lim f(x) * lim g(x)

Question 5

lim f(x) / g(x)

Answer 5

lim f(x) / lim (gx)

if lim g(x) does not equal 0

Question 6

lim (f(x))ⁿ

Answer 6

(lim f(x))ⁿ

Question 7

lim x^1/2

^{x → a}

Answer 7

a^1/2

If n is even, then a must equal to or greater than 0.

Question 8

lim (f(x))^1/2

Answer 8

(lim f(x))^1/2

Question 9

lim c

x → a

Answer 9

c

Question 10

lim x

x → a

Answer 10

a

Question 11

lim xⁿ

^{x → a}

Answer 11

aⁿ

Question 12

Does the limit exist?

lim f(x) = lim f(x)

x→a^- x→a⁺

Answer 12

Yes.

The limits meet at ‘a’ coming from the left and the right.