Limit as X approaches Infinity of ((x + sin(x) / x ln (x)) (2x + 1)

[tnick03]

The problem that I am struggling with is lim as x approaches infinity of ((x + sin(x) / x ln (x)) (2x + 1). I'm not very good with limits. Do I need to see what each part does as x approaches infinity? If so what do I do with that? Very confused please help.

 

[Steven G]

The problem that I am struggling with is lim as x approaches infinity of ((x + sin(x) / x ln (x)) (2x + 1). I'm not very good with limits. Do I need to see what each part does as x approaches infinity? If so what do I do with that? Very confused please help.

\(\displaystyle (x + \dfrac{sin(x)}{x ln (x)})(2x+1)\) (I assume this is what you meant)

\(\displaystyle x\rightarrow\infty\), \(\displaystyle -1\leqq sin(x) \leqq 1, x ln(x)\rightarrow\infty \ \ and \ \ (2x+1)\rightarrow\infty\)

Put this altogether.