Category: Limits

Question Number 162775 by john_santu last updated on 01/Jan/22 $$\underset{x\to 0}{\lim }\frac{a\sin 3x-b\sin 2x}{x^3}=\frac{1}{2}$$$$Findaandb.$$ Answered by mr W last updated on 01/Jan/22 $$=\underset{{x}\rightarrow\mathrm{0}}…

Question Number 31676 by gunawan last updated on 12/Mar/18 $$\mathrm{Given}\mathrm{function}f\mathrm{diferensiabel}\mathrm{on}\mathbf{R}.$$$$\mathrm{If}\underset{x\to 0}{\lim }f(\frac{a}{x}+b)\mathrm{non}\mathrm{zero}$$$$\underset{x\to 0}{\lim }[f(\frac{a}{x}+b)-\frac{a}{x}{f}^{\prime }(\frac{a}{x}+b)]=a$$$$\mathrm{how}\mathrm{many}\mathrm{value}\underset{x\to \mathrm{\infty }}{\lim }f\left(x\right)$$ Terms of Service Privacy…

Question Number 162747 by tounghoungko last updated on 01/Jan/22 Answered by bobhans last updated on 01/Jan/22 $$\mathrm{Happy}\mathrm{New}\mathrm{Year}\mathrm{too}$$$$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\mathrm{7x}−\mathrm{7x}+\mathrm{7x}−\mathrm{7sin}\:\mathrm{x}}{\mathrm{x}^{\mathrm{3}} \left(\frac{\mathrm{sin}\:\mathrm{x}}{\mathrm{x}}\right)^{\mathrm{3}} }\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{7}\left(\mathrm{x}−\mathrm{sin}\:\mathrm{x}\right)}{\mathrm{x}^{\mathrm{3}} }+\mathrm{7}^{\mathrm{3}} .\underset{{x}\rightarrow\mathrm{0}}…

Question Number 162718 by qaz last updated on 31/Dec/21 $$\underset{\mathrm{n}\to \mathrm{\infty }}{\lim }\frac{{\int }_{ϵ}^1{(1-{\mathrm{x}}^2)}^{\mathrm{n}}\mathrm{dx}}{{\int }_0^1{(1-{\mathrm{x}}^2)}^{\mathrm{n}}\mathrm{dx}}=?(0<ϵ<1)$$ Terms of Service Privacy…

Question Number 162643 by tounghoungko last updated on 31/Dec/21 $$\underset{x\to \mathrm{\infty }}{\lim }{x}^{4/3}(\sqrt[3]{x^2+1}+\sqrt[3]{3-x^2})=?$$ Answered by Ar Brandon last updated on 31/Dec/21 $$\mathscr{L}=\underset{{x}\rightarrow\infty}…