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Category: Limits

l-x-0-im-f-x-1-1-x-f-1-f-1-help-me-

Question Number 100343 by student work last updated on 26/Jun/20 $$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{l}im}\:\frac{\mathrm{f}\left(\mathrm{x}+\mathrm{1}\right)^{\frac{\mathrm{1}}{\mathrm{x}}} }{\mathrm{f}\left(\mathrm{1}\right)}\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{f}\left(\mathrm{1}\right)=? \\ $$$$\mathrm{help}\:\mathrm{me} \\ $$ Commented by student work last updated on 26/Jun/20…

lim-x-pi-2-cos-x-sin-x-sin-x-cos-x-1-3-

Question Number 165868 by cortano1 last updated on 09/Feb/22 $$\:\:\:\:\:\underset{{x}\rightarrow\frac{\pi}{\mathrm{2}}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\mathrm{x}}{\mathrm{sin}\:\mathrm{x}−\sqrt[{\mathrm{3}}]{\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}}}\:=? \\ $$ Answered by qaz last updated on 10/Feb/22 $$\underset{\mathrm{x}\rightarrow\frac{\pi}{\mathrm{2}}} {\mathrm{lim}}\frac{\mathrm{cos}\:\mathrm{x}}{\mathrm{sin}\:\mathrm{x}−\sqrt[{\mathrm{3}}]{\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}}} \\ $$$$=\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{−\mathrm{sin}\:\mathrm{x}}{\mathrm{cos}\:\mathrm{x}−\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\mathrm{x}−\mathrm{sin}\:\mathrm{x}}}…

lim-x-0-1-x-ln-1000-1-x-x-1001-

Question Number 34755 by Joel579 last updated on 10/May/18 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\frac{\mathrm{1}}{{x}}\:−\:\frac{\mathrm{ln}^{\mathrm{1000}} \:\left(\mathrm{1}\:+\:{x}\right)}{{x}^{\mathrm{1001}} }\right) \\ $$ Commented by Joel579 last updated on 10/May/18 $${L}\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}}{{x}}\left(\mathrm{1}\:−\:\frac{\mathrm{ln}^{\mathrm{1000}} \:\left(\mathrm{1}\:+\:{x}\right)}{{x}^{\mathrm{1000}}…

lim-x-pi-2-4sin-x-6-sin-x-10-pi-2-x-

Question Number 100134 by bemath last updated on 25/Jun/20 $$\underset{{x}\rightarrow\frac{\pi}{\mathrm{2}}} {\mathrm{lim}}\:\frac{\mathrm{4sin}\:\mathrm{x}−\sqrt{\mathrm{6}\sqrt{\mathrm{sin}\:\mathrm{x}}+\mathrm{10}}}{\frac{\pi}{\mathrm{2}}−\mathrm{x}}\:? \\ $$ Commented by bobhans last updated on 25/Jun/20 $$\mathrm{set}\:\frac{\pi}{\mathrm{2}}−\mathrm{x}\:=\:\mathrm{t}\:,\:\mathrm{x}\:=\frac{\pi}{\mathrm{2}}−\mathrm{t}\: \\ $$$$\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{4cos}\:\mathrm{t}−\sqrt{\mathrm{6}\sqrt{\mathrm{cos}\:\mathrm{t}}+\mathrm{10}}}{\mathrm{t}}\:= \\…