Question

Help me pleasseeeee!!! its about algebraic properties of limits!

Answer 1

`\text{Hello there! :)}`

`3. √(2) \\\\\text{4. 0}\\\\\text{5. dne}`

`\text{To find the overall limit, they must approach the same y-value from each side:}`

`\\\\3. \lim_{x \to (\pi )/(4) } 2sinx ={√(2)`

`\text{Therefore:}\\\\3. \lim_{x \to (\pi )/(4) } f(x)= {√(2) }`

`\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:}\\\\`

`\lim_(x \to \pi +) tanx = 0\\\\\text{So:}\\\\ \lim_(x \to \pi +) f(x) = 0`

`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})`