Consider the following information.

Question

Consider the following information.

lim x→c f(x)	=	4
lim x→c g(x)	=
7
6

Use the information to evaluate the limits.

(a)

lim x→c [6f(x)]

(b)

lim x→c [f(x) + g(x)]

(c)

lim x→c [f(x) g(x)]

(d)

lim x→c f(x)

g(x)

Answer 1

if

lim x→c [f(x)] = 4      and

lim x→c [g(x)] = 7

then 

(a)

lim x→c [6 f(x)] = 6  lim x→c [f(x)] = 6 * 4 = 24

(b)

lim x→c [f(x) + g(x)] = lim x→c [f(x) ] + lim x→c [g(x)]

                                          = 4                           + 7

                                          = 11

  (c)

lim x→c [f(x) g(x)] = lim x→c [f(x)] * lim x→c [g(x)]

                           =  4                 *    7                 =28

(d)

lim x→c [f(x) / g(x) ] = lim x→c [f(x) ] /  lim x→c [g(x) ]      only if  lim x→c [g(x) ] not equal 0

                                          =          4 /7