Provide an Appropriate Response $\lim _ { x \rightarrow } \frac { \ln ( x + 1 ) } { \ln x } = \lim _ { x \rightarrow } \frac { \ln ( x + 9982 ) } { \ln x }$

question 128

Essay

Provide an appropriate response.
-Show that $\lim _ { x \rightarrow } \frac { \ln ( x + 1 ) } { \ln x } = \lim _ { x \rightarrow } \frac { \ln ( x + 9982 ) } { \ln x }$ . Explain why this is the case.

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Definitions:

Adjustable Opening

A feature or mechanism that allows the size of an opening to be modified or adjusted as needed.

Accommodation of the Lens

The process by which the eye's lens changes shape to focus near or far objects on the retina.

Dilation of the Pupil

The process where the pupil enlarges to allow more light to enter the eye, often in response to low light conditions or certain emotional states.

Chemical Changes

Reactions that result in the transformation of substances into one or more different substances, involving the making and breaking of chemical bonds.