[tex]\text{Hello there! :)}[/tex]
[tex]3. \sqrt{2} \\\\\text{4. 0}\\\\\text{5. dne}[/tex]
[tex]\text{To find the overall limit, they must approach the same y-value from each side:}[/tex]
[tex]\\\\3. \lim_{x \to \frac{\pi }{4} } 2sinx ={\sqrt{2}[/tex]
[tex]\text{Therefore:}\\\\3. \lim_{x \to \frac{\pi }{4} } f(x)= {\sqrt{2} }[/tex]
[tex]\text{For this question, evaluate the limit from the RIGHT-HAND side:}\\\\4. \lim_{x \to \pi +} f(x)\\\\ \text{Use the equation tanx to evaluate since it involves values greater than \pi:}\\\\[/tex]
[tex]\lim_{x \to \pi +} tanx = 0\\\\\text{So:}\\\\ \lim_{x \to \pi +} f(x) = 0[/tex]
[tex]5. \\\\\text{Evaluate the overall limit. Make sure both sides approach the same y=value:}\\\\ \lim_{x \to \pi } 2cosx= -2\\\\ \lim_{x \to \pi } tanx = 0\\\\ \text{ Therefore:}\\ \lim_{x \to \pi } f(x) = dne \text{ (Does not exist})[/tex]
