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Calculus Gang: Limits, Continuity, and Discontinuity Fun!

Dive into calculus problems on limits, continuity, and discontinuity. Practice finding limits, identifying discontinuities, writing piecewise functions, and finding tangent and normal lines.

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Calculus Gang: Limits, Continuity, and Discontinuity Fun!

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  1. Calculus Gang Get in groups of three. Hopefully these problems will not take you to the limit of learning. 

  2. #1 • Find the limit If it exists

  3. #2 • Find the limit.

  4. #3 Give any points (x) where f(x) is not continuous and tell what type of discontinuity exists at that point.

  5. #4 • Write a piecewise function that would remove the discontinuity.

  6. #5 • Find the equation of the tangent line (if it exists) at x=3

  7. #6 • Find the equation of the normal line at x=1 for

  8. Answers • 1) 7 • 2) positive infinity • 3) x=5; point discontinuity; x=-5 jump discontinuity • 4) • 5) Does not exist; left and right hand derivative do not match. • 6) y-6=-1/2(x-1)

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