こんにちは。今回は数IIIで覚えておきたいグラフたちの指数関数編をやっていきます。グラフの概形関連づけて覚えておくと何かと便利です。それではどうぞ。
のグラフ
とすると,
となるのは,
となるのは,
極値に関して
![Rendered by QuickLaTeX.com x=-1](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-7edba747bcbd8a68875d9a9268b1c527_l3.png)
![Rendered by QuickLaTeX.com -\dfrac1e](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-1119f5c970910cb3e141bd12ed4015d7_l3.png)
極大値なし
変曲点
![Rendered by QuickLaTeX.com \left(-2,-\dfrac{2}{e^2}\right)](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-b2ac068f908d86829c6323a5f781df94_l3.png)
漸近線
![Rendered by QuickLaTeX.com y=0](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-f6f465e0f12abc1eee8e266b91926f96_l3.png)
![Rendered by QuickLaTeX.com x](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-5f16b0dcec027c9742e11d99170299a8_l3.png)
![Rendered by QuickLaTeX.com \displaystyle \lim_{x\to-\infty}xe^x=0](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-e5496a02a88165abf16a98f3444431c0_l3.png)
![Rendered by QuickLaTeX.com x=-t](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-0b7c14dd5381342817c2b1f4bcc5e8e3_l3.png)
![Rendered by QuickLaTeX.com x\to-\infty](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-d858587450d63b5d2fba697bf8b6b510_l3.png)
![Rendered by QuickLaTeX.com t\to\infty](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-635137428da54b5ed31452c295f0da29_l3.png)
![Rendered by QuickLaTeX.com \displaystyle\lim_{x\to-\infty}xe^x=\displaystyle\lim_{t\to\infty}-te^{-t}=\displaystyle\lim_{t\to\infty}-\dfrac{t}{e^t}=0](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-5f9b15ed3a6c0081c328cb8413a7b274_l3.png)
また,
![Rendered by QuickLaTeX.com x\to\infty](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-a1de85bca8bb98999926d51fd15684b4_l3.png)
![Rendered by QuickLaTeX.com f(x)\to\infty](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-371fb1e3391d34c4794bb1c325466dd6_l3.png)
のグラフ
とすると,
となるのは,
より,
となるのは,
より,
極値に関して
![Rendered by QuickLaTeX.com x=0](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-4c2c95e89d8f5c6e0e66407c3fe20028_l3.png)
![Rendered by QuickLaTeX.com 0](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-a4edc37914d061c44ba37cf722f607af_l3.png)
![Rendered by QuickLaTeX.com x=-2](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-7b10c867497a73111d7e8705373cbcc7_l3.png)
![Rendered by QuickLaTeX.com \dfrac{4}{e^2}](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-5bab17a4a27b25895e23ecae5332d1be_l3.png)
変曲点
![Rendered by QuickLaTeX.com \left(-2-\sqrt2, (6+4\sqrt2)e^{-2-\sqrt2}\right)](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-7473642f4aac121498222fab17d40ebd_l3.png)
![Rendered by QuickLaTeX.com \left(-2+\sqrt2, (6-4\sqrt2)e^{-2+\sqrt2}\right)](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-03561c872aae71d132bbe01a1696c475_l3.png)
漸近線
![Rendered by QuickLaTeX.com y=0](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-f6f465e0f12abc1eee8e266b91926f96_l3.png)
![Rendered by QuickLaTeX.com x](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-5f16b0dcec027c9742e11d99170299a8_l3.png)
![Rendered by QuickLaTeX.com \displaystyle \lim_{x\to-\infty}x^2e^x=0](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-cb038263ca5fd1ed6c98483d6e3c4382_l3.png)
また,
![Rendered by QuickLaTeX.com x\to\infty](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-a1de85bca8bb98999926d51fd15684b4_l3.png)
![Rendered by QuickLaTeX.com f(x)\to\infty](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-371fb1e3391d34c4794bb1c325466dd6_l3.png)
のグラフ
とおくと,
となるのは,
となるのは,
極値に関して
![Rendered by QuickLaTeX.com x=1](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-8a4b1fabb9dd2ab5aece4bfdff8f5021_l3.png)
![Rendered by QuickLaTeX.com \dfrac1e](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-702249f607145a7aa682337cb6d6a53a_l3.png)
極小値なし
変曲点
![Rendered by QuickLaTeX.com \left(2,\dfrac{2}{e^2}\right)](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-3ec6d8f650f605a4f812af451d89ebd5_l3.png)
漸近線
![Rendered by QuickLaTeX.com y=0](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-f6f465e0f12abc1eee8e266b91926f96_l3.png)
![Rendered by QuickLaTeX.com x](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-5f16b0dcec027c9742e11d99170299a8_l3.png)
![Rendered by QuickLaTeX.com \displaystyle \lim_{x\to\infty}\dfrac{x}{e^x}=0](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-8291d1fc4fe827f67c14189258ce148f_l3.png)
また,
![Rendered by QuickLaTeX.com x\to-\infty](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-d858587450d63b5d2fba697bf8b6b510_l3.png)
![Rendered by QuickLaTeX.com f(x)\to-\infty](https://mathtext.info/blog/wordpress/wp-content/ql-cache/quicklatex.com-37225a89f5d81981d4ad235b8494d0af_l3.png)