Calculus

Curve Sketching

Vertical Asymptotes

         

Evaluate limx1+(2x21+2). \displaystyle{\lim_{x \to 1^+} \left (\frac{2}{ x^2 - 1 }+2 \right ) }.

What are the vertical asymptotes of y=3+6xx225? y = 3 + \frac{6x}{x^2-25} ?

What is the number of vertical asymptotes of y=5x2x29+4? y = \frac{5x^2}{x^2-9} + 4 ?

Find the sum of the yy-coordinates of all the distinct intersection points between y=x+1y=x+1 and the vertical asymptotes of the curve: y=x+5x310x2+33x36.y=\frac{x+5}{x^3-10x^2+33x-36}.

What is the number of vertical asymptotes of y=5x2x225+5? y = \frac{5x^2}{x^2-25} + 5 ?

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