finding the following limits.... 3 more ?

Question

hi,

i would like to find out how to solve this problem

i would like to find out given that the limit of the function f(x)=6 as x approaches 1 and limit of the function g(x)=4 i would like to find out how to find the following limits (if they exist)

lim 3f(x) + g(x) / f(x)+2g(x) as x approaches 1
lim square root f(x) as x approaches 1 and finally
lim f(x) square root g(x) as x approaches 1

thanks again for your help. it is much appreciated

Answer 1

darn, calculus!!

well, since f(x) and g(x) are cxonstants for all x in R, then it's limits are constants as well...

so...

lim as x approaches 1 of 6 = 6
lim as x approaches 1 of 4 = 4

so...

lim as x approaches 1 of 3f(x) + g(x) / f(x)+2g(x) = lim as x approaches 1 of 3(6) + (4) / (6)+(4) = 22/10 = 2.2

lim square root f(x) as x approaches 1 = lim square root (6) as x approaches 1 = sqrt(6)

lim f(x) square root g(x) as x approaches 1 = lim (6) square root (4) as x approaches 1 = 6*2 = 12

Answer 2

lim 3f(x) + g(x) / f(x)+2g(x) as x approaches 1
= 3*6+4/6+2*4=26+2/3=80/3
lim square root f(x) as x approaches 1
= square root (6)
lim f(x) square root g(x) as x approaches 1
= square root (4)

Answer 3

1)findin the lmt.
lim.x->1 [3f(x) + g(x)/(f(x)+2g(x))
=3*6 + 4/(6+2*4)
=22/14
=11/7
2)limx->1 sq.rtf(x)
=sq. rt.6
3)limx-> sq.rt g(x)
=sq. rt 4=2