Question Number 128038 by Walt123 last updated on 03/Jan/21 | ||
$$ \\ $$ Resolva a equação abaixo:\\n$$ \\ $$ $$\mathrm{5}^{\mathrm{x}} .\mathrm{16}^{\frac{\mathrm{x}−\mathrm{1}}{\mathrm{x}}} =\mathrm{100} \\ $$ | ||
Answered by MJS_new last updated on 03/Jan/21 | ||
$$\mathrm{5}^{{x}} \mathrm{16}^{\mathrm{1}−\frac{\mathrm{1}}{{x}}} =\mathrm{100} \\ $$ $$\mathrm{5}^{{x}} \mathrm{16}^{−\frac{\mathrm{1}}{{x}}} =\frac{\mathrm{25}}{\mathrm{4}} \\ $$ $${x}\mathrm{ln}\:\mathrm{5}\:−\frac{\mathrm{1}}{{x}}\mathrm{ln}\:\mathrm{16}\:=\mathrm{ln}\:\frac{\mathrm{25}}{\mathrm{4}} \\ $$ $${x}^{\mathrm{2}} −\frac{\mathrm{2ln}\:\frac{\mathrm{5}}{\mathrm{2}}}{\mathrm{ln}\:\mathrm{5}}{x}−\frac{\mathrm{4ln}\:\mathrm{2}}{\mathrm{ln}\:\mathrm{5}}=\mathrm{0} \\ $$ $${x}=−\frac{\mathrm{2ln}\:\mathrm{2}}{\mathrm{ln}\:\mathrm{5}}\vee{x}=\mathrm{2} \\ $$ | ||
Answered by rodrigue last updated on 03/Jan/21 | ||
$$ \\ $$ $${need}\:{help}\:{i}\:{don}'{t}\:{know}\:{to}\:{create}\:{new}\:{subject} \\ $$ $$\underset{{x}\rightarrow\Pi} {\mathrm{lim}}\:\frac{\mathrm{2}{sin}\mathrm{2}{x}}{{cosx}\:+\mathrm{1}} \\ $$ | ||
Commented byliberty last updated on 03/Jan/21 | ||
$$\:\underset{{x}\rightarrow\pi} {\mathrm{lim}}\:\frac{\mathrm{2sin}\:\mathrm{2x}}{\mathrm{cos}\:\mathrm{x}+\mathrm{1}}\:;\:\mathrm{let}\:\mathrm{x}=\pi+\mathrm{t} \\ $$ $$\:\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2sin}\:\left(\mathrm{2}\pi+\mathrm{2t}\right)}{\mathrm{cos}\:\left(\pi+\mathrm{t}\right)+\mathrm{1}}\:=\:\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2sin}\:\mathrm{2t}}{−\mathrm{cos}\:\mathrm{t}+\mathrm{1}} \\ $$ $$\:\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2sin}\:\mathrm{2t}}{\mathrm{2sin}\:^{\mathrm{2}} \left(\frac{\mathrm{t}}{\mathrm{2}}\right)}\:=\:\infty\: \\ $$ $$\mathrm{L}'\mathrm{Hopital}\:\Rightarrow\:\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{4cos}\:\mathrm{2t}}{\mathrm{sin}\:\mathrm{t}}\:=\:\infty\: \\ $$ | ||
Commented byrodrigue last updated on 04/Jan/21 | ||
$$ \\ $$ $${thanks} \\ $$ | ||