Question

evaluate the limit.
lim 1+8x/10-3x
x->inf

Answer 1

8/-3

Answer 2

-8/3

Answer 3

-8/3

Answer 4

or if you prefer
\[-\frac{8}{3}\]

Answer 5

if you divide by x you get \[\lim x->\infty (1/x+8)/(10/x-3)\]but the lim x->inf of a constant/x is zero
so you get (0+8)/(0-3)

Answer 6

\[{1+8x \over10-3x} = {x(8 + {1\over x}) \over x(-3 + {10 \over x}) } = {8 + {1\over x} \over -3 + {10 \over x} }\]
\[\implies \lim_{x\rightarrow \infty}{1+8x \over10-3x} = \lim_{x\rightarrow \infty}{8 + {1\over x} \over -3 + {10 \over x} } =\ ?\]

Answer 7

thanks guys i appreciate the help and the step by process!