Calculus Calculus Math Forum

 April 22nd, 2012, 02:15 AM #1 Member   Joined: Apr 2012 Posts: 64 Thanks: 0 2 limits questions..please help I need help evaluating these two limits 1) lim (x tends towards 2) (x-2) (absolute value) / x-2 2) lim (x tends towards zero) Square root of the absolute value of x multiplied by e^(sin pi/x)
 April 22nd, 2012, 02:56 AM #2 Senior Member   Joined: Jul 2011 Posts: 227 Thanks: 0 Re: 2 limits questions..please help $\lim_{x \to 2} \frac{|x-2|}{x-2}$ Consider two cases (by definition of the absolut value): 1) $x-2>0 \Leftrightarrow x>2$ thus $|x-2|=x-2$, in that case $\lim_{x \downarrow 2} \frac{|x-2|}{x-2}=\lim_{x \downarrow 2} \fra{x-2}{x-2}=1$. 2) $x-2<0 \Leftrightarrow x<2$ thus $|x-2|=-(x-2)=2-x$, in that case $\lim_{x \uparrow 2} \frac{|x-2|}{x-2}=\lim_{x \uparrow 2} \frac{2-x}{x-2}=-1$ Therefore the limiet doesn't exist. Try to do something similar for the second one.
 April 22nd, 2012, 03:14 AM #3 Member   Joined: Apr 2012 Posts: 64 Thanks: 0 Re: 2 limits questions..please help Thank you, I understand it now .. The second one is zero, I had a go at it ..

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