AP Calculus

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Nora, Abigail, and Emma are studying for their calculus exam. They are analyzing the function f(x). Can you help them figure out the properties of this function? Check all that apply:

• f(x) has a non-removable discontinuity at x=2

• f(x) has a removable discontinuity at x=-2

• f(x) is continuous at x=-2

Ethan, Nora, Maya, and James are on a school trip to a historical museum. They found a mysterious box in an exhibit. The box has a lock with four options. To unlock it and reveal the artifact inside, they need to select all the correct options. Can you help them?

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A 15-feet-long ladder leaning against a vertical wall. The ladder starts sliding down the wall at a constant rate of 2 feet per second. At what rate is the angle between the bottom of the ladder and the ground changing when the bottom of the ladder is 9 feet from the base of the wall?

Imagine this: Elijah, Hannah, and Michael are helping Santa with his sleigh. The sleigh is flying with a velocity given by v(t)=2cos(3t). They are curious to know the distance traveled from the moment it took off (t=0) to the first time it stops. Can you help them figure it out?