[Music] Making art was something she seems to have done in opposition to her family, but she also was inately talented and you look at the early drawings and they are completely exquisite. The...

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Why is the sky dark at night? You might think the answer is obvious - the sun isn't up! But the only reason the sky looks blue during the day is that sunlight scatters off of the atmosphere -...

I have been asked to be the last speaker of today. I know, of course, that you will all be extremely tired at this moment. But the fun thing is that I'll be talking about logic and creativity....

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The eternal bond you gave me is not something I can file away as a memory. Because you taught me about compassion I discovered true strength, thank you. Proud of what I had mistaken to be dexterity...

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- WELCOME TO FOUR EXAMPLES OF DETERMINING BASIC LIMITS. WE FIRST HAVE THE LIMIT AS X APPROACHES -2 OF 4. SO NOTICE FOR THIS EXAMPLE WE'RE USING THE CONSTANT FUNCTION F OF X = 4 TO DETERMINE...

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Let's take a look at this limit. The limit as x goes to 4 of 3 minus 2x over x minus 4 times x plus 2. We can start just by plugging in 4 and see what we get. If I plug in 4 to the top,...

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It's finnaly here! With the new "Sparky", and it's hydraulic ball bearings, you will defeat everyone that comes in your way! Sparky! Having trouble with the ladies?...

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We've just learned a bunch of laws for computing limits, but unfortunately usually limits are not given exactly in the form that we could apply one of these laws. One example of a kind of...

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[music] Let's integrate x squared from 0 to 1 by using the definition of integral. Now, since the function x squared is continuous, it's integrable. So, it won't matter exactly...

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[SOUND] Let's think back to our friend the square root function. What's the square root of two? Well, the square root of two is about 1.414. What's the square root of 2.01?...

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