In this segment of the course we are going to talk about 3D rotations. 3D rotations is a topic that has engaged many of the greatest minds of our civilization over centuries. It's also a topic...
[MUSIC]. Let's compute the volume of a bead but first we have to figure out how we're going to build the bead as a solid of revolution. So start with the X, Y plane and I'm...

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- WE'RE GIVEN THE LOGARITHMIC FUNCTION F OF X = LOG BASE 5 OF X AND ASKED A VARIETY OF QUESTIONS ABOUT THE PROPERTIES AND CHARACTERISTICS OF THE FUNCTION. BEFORE WE ANSWER THE QUESTIONS,...
[MUSIC]. Let's figure out the volume of a certain solid of revolution. For example, let's think about this region inside here, the region that's below the graph of y equals the...
♫Theme song♫ DORA: Hola, soy Dora. BOOTS: And I'm Boots! DORA: And today, we're going to LaSalle Mountain, LaSalle Montaña! Can you say montaña? *Pause* Great! Will you help me get to...
- WE'RE ASKED TO DETERMINE THE END BEHAVIOR OR LONG RUN BEHAVIOR FOR EACH FUNCTION. THE END BEHAVIOR, OR LONG RUN BEHAVIOR, DESCRIBES THE VALUE OF THE FUNCTION OR THE Y VALUE AS X APPROACHES...

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- WE WANT TO EVALUATE THE GIVEN DEFINITE INTEGRAL USING A GEOMETRIC FORMULA. SO TO REVIEW, IF A FUNCTION F OF X IS CONTINUOUS AND NON-NEGATIVE ON A CLOSED INTERVAL FROM A TO B, THEN THE AREA UNDER THE...