Join IDNLearn.com to access a wealth of knowledge and get your questions answered by experts. Ask anything and receive well-informed answers from our community of experienced professionals.
Sagot :
The Solution:
Given the functions below:
[tex]-\ln (x)\text{ and }\frac{1}{x}[/tex]We are required to tell which of them will go to infinity faster as x tends to positive zero.
we shall examine each of the two functions by investigating their slopes under the given conditions.
[tex]\begin{gathered} T\text{he derivative of -}\ln (x)\text{ is }\frac{-1}{x}\text{ , while that of} \\ \frac{1}{x}\text{ is }\frac{-1}{x^2} \end{gathered}[/tex]Comparing the absolute values of their slopes at positive smaller values of x, (at x<1 , we get
[tex]\begin{gathered} |\frac{-1}{x^2}|>|\frac{-1}{x}| \\ \text{Clearly, the function }\frac{1}{x}\text{ goes to }\infty\text{ faster as x}\rightarrow0^+ \end{gathered}[/tex]Therefore, the correct answer is 1/x
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. Your questions deserve precise answers. Thank you for visiting IDNLearn.com, and see you again soon for more helpful information.
