Calculate, to four decimal places, the first eight terms of the recursive sequence. Does it appear to be convergent? If so, guess the value of the limit. Then assume the limit exists and determine its exact value. $a_{1}=1, a_{n+1}=\frac{6}{1+a_{n}}$

The Michaelis-Menten equation models the rate v of an enzymatic reaction as a function of the concentration [S] of a substrate S. In the case of the enzyme chymotrypsin the equation is $v=\frac{0.14[\mathrm{S}]}{0.015+[\mathrm{S}]}.$ What is the horizontal asymptote of the graph of v? What is its significance?

Prove that $\lim _ { x \rightarrow 0 } x ^ { 2 } \cos \left( 1 / x ^ { 2 } \right) = 0$

Determine the infinite limit. $\lim _{x \rightarrow-3^{-}} \frac{x+2}{x+3}$

If $2 x \leqslant g(x) \leqslant x^{4}-x^{2}+2$ for all x, evaluate $\lim _{x \rightarrow 1} g(x)$

Calculate, to four decimal places, the first eight terms of the recursive sequence. Does it appear to be convergent? If so, guess the value of the limit. Then assume the limit exists and determine its exact value. $a_{1}=1, a_{n+1}=\sqrt{5 a_{n}}$