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1. Find the limit as x approaches 0 , of the function (1- cos x)/x^2. (5 mks)
2.find the limit as x approaches y, of the function (((sin^2 x) -(sin^2 y))/(x^2 -y^2)). 6mks

Respuesta :

LammettHash
[tex]\displaystyle\lim_{x\to0}\frac{1-\cos x}{x^2}=\lim_{x\to0}\frac{1-\cos^2x}{x^2(1+\cos x)}=\lim_{x\to0}\frac{\sin^2x}{x^2(1+\cos x)}[/tex]
[tex]=\displaystyle\lim_{x\to0}\frac{\sin^2x}{x^2}\cdot\lim_{x\to0}\frac1{1+\cos x}=\left(\lim_{x\to0}\frac{\sin x}x\right)^2\lim_{x\to0}\frac1{1+\cos x}=1^2\cdot\frac1{1+1}=\frac12[/tex]

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