Category: Limits

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Question Number 11444 by Joel576 last updated on 26/Mar/17 $$\mathrm{If}\underset{x\to 0}{\lim }\frac{\sqrt{px+q}-2}{x}=1$$$$\mathrm{What}\mathrm{is}\mathrm{the}\mathrm{value}\mathrm{of}p+q?$$ Answered by ajfour last updated on 26/Mar/17 $$\mathrm{then}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{q}}\left(\mathrm{1}+\mathrm{px}/\mathrm{q}\right)^{\mathrm{1}/\mathrm{2}} \:−\mathrm{2}}{\mathrm{x}}\:=\mathrm{1}…

Question Number 11416 by anisa last updated on 25/Mar/17 Answered by Joel576 last updated on 25/Mar/17 $$=\underset{x\to 0}{\lim }\frac{2{\sin }^{2}x}{2x\sin 2x}$$$$=\underset{x\to 0}{\lim }\frac{2}{2}.\frac{\sin x}{x}.\frac{\sin x}{\sin 2x}$$$$=\:\mathrm{1}\:.\:\mathrm{1}\:.\:\frac{\mathrm{1}}{\mathrm{2}} \…

Question Number 11395 by Joel576 last updated on 23/Mar/17 $$\mathrm{Prove}\mathrm{that}\mathrm{those}\mathrm{functions}\mathrm{below}{\mathrm{don}}^{\prime }\mathrm{t}\mathrm{have}\mathrm{limit}$$$$\mathrm{a})\underset{(x,y)\to (0,0)}{\lim }\frac{xy}{x^2+y^2}$$$$$$$$b)\underset{(x,y)\to (0,0)}{\lim }\frac{xy+y^3}{x^2+y^2}$$…