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Curve Sketching

You don't need a calculator or computer to draw your graphs! Derivatives and other Calculus techniques give direct insights into the geometric behavior of curves.

Vertical Asymptotes

         

Evaluate \( \displaystyle{\lim_{x \to 1^+} \left (\frac{2}{ x^2 - 1 }+2 \right ) }.\)

What are the vertical asymptotes of \[ y = 3 + \frac{6x}{x^2-25} ?\]

What is the number of vertical asymptotes of \[ y = \frac{5x^2}{x^2-9} + 4 ?\]

Find the sum of the \(y\)-coordinates of all the distinct intersection points between \(y=x+1\) and the vertical asymptotes of the curve: \[y=\frac{x+5}{x^3-10x^2+33x-36}.\]

What is the number of vertical asymptotes of \[ y = \frac{5x^2}{x^2-25} + 5 ?\]

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