exercise:60af2b75f8: Difference between revisions
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(Created page with "<div class="d-none"><math> \newcommand{\ex}[1]{\item } \newcommand{\sx}{\item} \newcommand{\x}{\sx} \newcommand{\sxlab}[1]{} \newcommand{\xlab}{\sxlab} \newcommand{\prov}[1] {\quad #1} \newcommand{\provx}[1] {\quad \mbox{#1}} \newcommand{\intext}[1]{\quad \mbox{#1} \quad} \newcommand{\R}{\mathrm{\bf R}} \newcommand{\Q}{\mathrm{\bf Q}} \newcommand{\Z}{\mathrm{\bf Z}} \newcommand{\C}{\mathrm{\bf C}} \newcommand{\dt}{\textbf} \newcommand{\goesto}{\rightarrow}...") |
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Assume that <math>a > 1</math>. | Assume that <math>a > 1</math>. | ||
<ul style{{=}}"list-style-type:lower-alpha" | <ul style{{=}}"list-style-type:lower-alpha"> | ||
<li> | <li> | ||
Using the definition of <math>a^x</math>, show that | Using the definition of <math>a^x</math>, show that | ||
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</math></li> | </math></li> | ||
<li> | <li> | ||
Using the result of | Using the result of (a), prove that | ||
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Using | Using (a), show that | ||
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< | <li> | ||
Using (b), show that | |||
Using | |||
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<li>What do | <li>What do (a), (b), (c), and (d) say geometrically about the graph of the function <math>a^x</math>?</li> | ||
and | |||
of the function <math>a^x</math>?</li> | |||
</ul> | </ul> | ||
Latest revision as of 22:38, 23 November 2024
[math]
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[/math]
Assume that [math]a \gt 1[/math].
-
Using the definition of [math]a^x[/math], show that
[[math]] \lim_{x\goesto\infty} a^x = \infty . [[/math]]
-
Using the result of (a), prove that
[[math]] \lim_{x\goesto-\infty} a^x = 0 . [[/math]]
-
Using (a), show that
[[math]] \lim_{x\goesto\infty} \frac{d}{dx} a^x = \infty . [[/math]]
-
Using (b), show that
[[math]] \lim_{x\goesto-\infty} \frac{d}{dx} a^x = 0 . [[/math]]
- What do (a), (b), (c), and (d) say geometrically about the graph of the function [math]a^x[/math]?