Limit Laws

Question 1

lim(x->c) (f(x) + g(x))

Answer 1

L + M

Question 2

lim(x->c) (f(x) - g(x))

Answer 2

L - M

Question 3

lim(x->c) (k . f(x))

Answer 3

k . L

Question 4

lim(x->c) (f(x) . g(x))

Answer 4

L . M

Question 5

lim(x->c) (f(x)/g(x))

Answer 5

L/M, M does not = 0

Question 6

lim(x->c) (f(x))^n

Answer 6

L^n, where n is a positive integer

Question 7

lim(x->c) nrt(f(x))

Answer 7

nrt(L) = L^(1/n), where n is a positive integer

Question 8

L’Hopital’s rule

Answer 8

Used to solve limits in indeterminate forms (0/0, INF/INF, 0xINF, INF–INF, 0^0, INF^0, 1^INF). If lim(x->a) f(x) = lim(x->a) g(x), f & g are differentiable in an open interval containing a, & g’(x) does not = 0 in an open interval if x does not = 1, then the lim(x->a) (f(x)/g(x)) = lim(x->a) (f’(x)/g’(x)).

Question 9

lim 0 * INF

Answer 9

lim f(x)g(x) = lim f(x)/(1/g(x)) = lim g(x)/(1/f(x))

Question 10

lim INF–INF

Answer 10

lim (f(x)-g(x)/sqrtf(x)-sqrtg(x))

Question 11

lim 0^0 or lim INF^0 or lim 1^INF

Answer 11

lim f(x)^g(x) = L, then: ln(L) = lim g(x)lnf(x) -> ln(L) = lim lnf(x)/(1/g(x))