A set of ordered pairs is called a relation. The set of all first components of the ordered pairs of a relation is the domain of the relation, and the set of all second components of the ordered pairs is the range of the relation. :)

4 0

3 years ago

Evaluate lim x→∞ (3x+1)^(4/x), using l'hospital's rule as needed. show all work using proper notation. as you show your work, if

Alborosie

$\displaystyle\lim_{x\to\inty}(3x+1)^{4/x}=\lim_{x\to\infty}e^{\ln(3x+1)^{4/x}}=e^{\lim\limits_{x\to\infty}\ln(3x+1)^{4/x}}$

$\displaystyle\lim_{x\to\infty}\ln(3x+1)^{4/x}=\lim_{x\to\infty}\frac{4\ln(3x+1)}x\stackrel{\mathrm{LHR}}=\lim_{x\to\infty}\frac{4\frac3{3x+1}}1=\lim_{x\to\infty}\frac{12}{3x+1}=0$

$\implies\displaystyle\lim_{x\to\infty}(3x+1)^{4/x}=e^0=1$

4 0

4 years ago