Find Each of the Following Limits or Explain Why It $\lim _ { x \rightarrow 1 ^ { + } } \frac { \ln ( 2 x ) } { \ln x }$

question 141

Short Answer

Find each of the following limits or explain why it does not exist.(a) $\lim _ { x \rightarrow 1 ^ { + } } \frac { \ln ( 2 x ) } { \ln x }$ (b) $\lim _ { x \rightarrow 0 } \frac { e ^ { - 2 x } - 1 } { x ^ { 2 } - x }$ (c) $\lim _ { x \rightarrow \frac { \pi } { 2 } } ( \sec x - \tan x )$

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Definitions:

Thalamus

A brain region that acts as a relay center, processing and transmitting information to the cerebral cortex.

Brainstem

The part of the brain connecting the spinal cord with the forebrain and cerebrum, responsible for controlling vital life functions.

Basal Ganglia

A group of nuclei in the brain involved in coordinating movement as well as learning, behavior, and emotions.

Corticospinal Tract

A pathway in the central nervous system that conducts impulses from the brain to the spinal cord, controlling voluntary muscle movements.