Mă puteți ajuta cu aceste două exerciții?
AniDeȘcoală.ro
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Please briefly explain why you feel this question should be reported.
Va rugam explicate, pe scurt, de ce credeti ca aceasta intrebare trebuie raportata.
Motivul pentru care raportezi utilizatorul.
2.
*** QuickLaTeX cannot compile formula: \[ \begin{array}{l} a) \\ Singura\;restrictie\;este\;ca\;x\;nu\;poate\;fi\;0\;din\;cauza\;lui\;\frac{1}{x}.\;Asadar\;D_{\max } = R^* . \\ f\left( { - x} \right) = - x - \frac{1}{x} = - \left( {x + \frac{1}{x}} \right) = - f\left( x \right) \Rightarrow f\;este\;functie\;impara. \\ b) \\ {\lim }\limits_{x \to \pm \infty } f\left( x \right) = \pm \infty + \frac{1}{{ \pm \infty }} = \pm \infty + 0 = \pm \infty \notin R. \Rightarrow nu\;are\;asimptote\;orizontale. \\ \\ y = mx + n \\ m = {\lim }\limits_{x \to \pm \infty } \frac{{f\left( x \right)}}{x} = {\lim }\limits_{x \to \pm \infty } \left( {1 + \frac{1}{{x^2 }}} \right) = 1 \in R^* . \\ n = {\lim }\limits_{x \to \pm \infty } \left( {f\left( x \right) - mx} \right) = {\lim }\limits_{x \to \pm \infty } \left( {x + \frac{1}{x} - x} \right) = {\lim }\limits_{x \to \pm \infty } \frac{1}{x} = 0 \in R. \\ Deci\;y = 1 \cdot x + 0 = x\;este\;asimptota\;la + \infty \;si\;la\; - \infty . \\ \\ {\lim }\limits_{x \to 0 \hfill \atop x > 0 \hfill} f\left( x \right) = {\lim }\limits_{ x \to 0 \hfill \atop x > 0 \hfill} \left( {x + \frac{1}{x}} \right) = 0 + \frac{1}{{0_ + }} = + \infty . \Rightarrow x = 0\;este\;asimptota\;verticala. \\ Analog\;se\;obtine\;ca\; {\lim }\limits_{x \to 0 \hfill \atop x < 0 \hfill} f\left( x \right) = - \infty ,\;insa\;nu\;este\;necesar\;sa\;o\;calculam,\;caci\;este\;suficient\;sa\;aratam\;ca\;unul\;dintre\;limite\;este\; + \infty \;sau\; - \infty . \\ Avem\; {\lim }\limits_{x \to x_0 } f\left( x \right) = x_0 + \frac{1}{{x_0 }} \in R,\;\forall x_0 \in R^* \Rightarrow functia\;nu\;mai\;are\;asimptote\;verticale. \\ \\ In\;concluzie,\;asimptotele\;sunt] *** Error message: Limit controls must follow a math operator. leading text: b) \\ {\lim }\limits Limit controls must follow a math operator. leading text: m = {\lim }\limits Limit controls must follow a math operator. leading text: ...c{{f\left( x \right)}}{x} = {\lim }\limits Limit controls must follow a math operator. leading text: n = {\lim }\limits Limit controls must follow a math operator. leading text: ...( x \right) - mx} \right) = {\lim }\limits Limit controls must follow a math operator. leading text: ... \frac{1}{x} - x} \right) = {\lim }\limits Limit controls must follow a math operator. leading text: \\ {\lim }\limits Limit controls must follow a math operator. leading text: ...\hfill} f\left( x \right) = {\lim }\limits Limit controls must follow a math operator.La prima problema trebuie sa derivezi functia si sa alegi a si b astfel incat x=0 si x=2 sa fie solutii a ecuatiei f'(x)=0, adica f'(0)=f'(2)=0.
Dreapta x=0 este asimptota verticala ,nu orizontala!
Aveti dreptate! Am corectat!