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Calculus

Curve Sketching

Concept Quizzes

Curve Sketching Warmup
Turning Points
Curve Sketching
Increasing / Decreasing Functions
Vertical Asymptotes
Relative Magnitude of Functions
Tangent to a Curve
Normal to a Curve

Challenge Quizzes

Curve Sketching: Level 3 Challenges
Curve Sketching: Level 4 Challenges

Vertical Asymptotes

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

0

-\infty

1

+\infty

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by Brilliant Staff

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

x= {-5}, {5}

x= {-5}

x= {10}

x= {-10}, {10}

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by Brilliant Staff

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

2 0 1 3

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by Brilliant Staff

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

10 12 7 9

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by Brilliant Staff

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

0 3 2 1

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by Brilliant Staff

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