Question

Finding Limits and Relative Extrema Use spreadsheet to complete the table using

Answer 1

Answer:

a) 0 b) Maximum (2<x<3, 0<y<1)

Step-by-step explanation:

a) Through the table we can estimate the value of the limit as 0, since it starts with 0 goes up and then goes down to 0

Verifying:

$\lim_{x\rightarrow \infty}\frac{ln(x)}{x}\Rightarrow \lim_{x\rightarrow \infty}\frac{\frac{\mathrm{d} }{\mathrm{d} x}[ln(x)]}{\frac{\mathrm{d} }{\mathrm{d} x}[x]}\Rightarrow \lim_{x\rightarrow \infty}\frac{\frac{1}{x}}{1}\Rightarrow \frac{\lim_{x\rightarrow \infty}1}{\lim_{x\rightarrow \infty}x}=0$

b) The Relative extrema was estimated here using Geogebra. Estimating  it considering [0,5] we could say: (2<x<3, 0<y<1). Calculating it using Geogebra applet:

$(e,\frac{1}{e})=(2.72,0.36)$