Limits

Question 1

sum rule: limₓ→c (f(x) + g(x)) =

Answer 1

limₓ→c (f(x)) + limₓ→c (g(x))

Question 2

difference rule: limₓ→c (f(x) - g(x)) =

Answer 2

limₓ→c (f(x)) - limₓ→c (g(x))

Question 3

product rule: limₓ→c (f(x) * g(x)) =

Answer 3

limₓ→c (f(x)) * limₓ→c (g(x))

Question 4

constant multiple rule: limₖ→c (k * g(x)) =

Answer 4

k * limₓ→c (g(x))

Question 5

quotient rule: limₓ→c (f(x) / g(x)) =

Answer 5

(limₓ→c (f(x)) / (limₓ→c (g(x))) provided limₓ→c (g(x)) ≠ 0

Question 6

power rule: limₓ→c (f(x))^n =

Answer 6

(limₓ→c (f(x))^n for n

Question 7

root rule: limₓ→c (n√f(x)) =

Answer 7

n√limₓ→c (f(x)) for n ≥ 2 a positive integer, provided n√limₓ→c (f(x)) and limₓ→c (n√f(x)) are real numbers

Question 8

limit that fails to exist:

Answer 8

limₓ→₀ (|x| / x)

Question 9

unbounded behavior:

Answer 9

limₓ→₀ (1/x^2) = doesn’t exist

Question 10

oscilating behavior:

Answer 10

limₓ→₀ (1/x) = doesn’t exist

Question 11

special limits (sin):

Answer 11

limₓ→₀ (sinx / x) = 1

Question 12

special limits (cos):

Answer 12

limₓ→₀ (1 - cosx / x) = 0