Question

what is the limit of sqrt (x^2-10x+1)-x as x approaches infinity

Answer 1

\[\lim_{x\rightarrow +\infty}\sqrt{x^2-10x+1}-x=\]\[=\lim_{x\rightarrow +\infty}\left(\sqrt{x^2-10x+1}-x\right)\cdot\frac{\sqrt{x^2-10x+1}+x}{\sqrt{x^2-10x+1}+x}=\]\[=\lim_{x\rightarrow +\infty}\frac{x^2-10x+1-x^2}{\sqrt{x^2-10x+1}+x}=\]\[=\lim_{x\rightarrow +\infty}\frac{-10x+1}{x\sqrt{1-10/x+1/x^2}+x}=\lim_{x\rightarrow +\infty}\frac{-10x+1}{2x}=-5\]

Answer 2

wow thanks very much

Answer 3

Let f(x)=x^3−2x. Calculate the difference quotient f(2+h)−f(2)/h for

h=.1
h=.01
h=−.01
h=−.1
if you can demonstrate how to do one, I will learn to do the rest

Answer 4

\[h=0.1\]\[f(2)=4\quad,\quad f(2+h)=f(2+0.1)=f(2.1)=5.061\]\[\frac{f(2+h)-f(2)}{h}=\frac{f(2.1)-f(2)}{0.1}=\frac{1.061}{0.1}=10.61\]