SOLUTION: a) evaluate lim x--> infinity (x-ln(x)) b) analyze f(x)= lx^3+x^2-6xl l.(f(x))..l=(absolute value)

Algebra ->  Equations -> SOLUTION: a) evaluate lim x--> infinity (x-ln(x)) b) analyze f(x)= lx^3+x^2-6xl l.(f(x))..l=(absolute value)      Log On


   

Question 1086385: a) evaluate
lim x--> infinity (x-ln(x))

b) analyze
f(x)= lx^3+x^2-6xl
l.(f(x))..l=(absolute value)
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
a) Lim x->infinity { x - ln(x) } = Lim x->infinity { +ln%28e%5Ex+%2F+x%29+ }
Let +u+=+e%5Ex+%2F+x+ (i.e. just look at the inside of ln() )
Lim x->infinity {u} = Lim u->infinity {u} ( letting x -> infinity is equivalent to letting u->infinity)
Lim u->infinity +%28ln%28u%29%29+ = infinity
Ans: The limit does not exist, it goes off to infinity.
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b) |x%5E3%2Bx%5E2-6x%29+| = | +x%28x%5E2%2Bx-6%29+ | = |+x%28x-2%29%28x%2B3%29+ |
Roots at x=-3, x=0, and x=2. The function is always >= 0. Graph below