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Virendrasingh D.

If $f(x)=x+\sqrt{2-x}$ and $g(u)=u+\sqrt{2-u},$ is it true that $f=g ?$

00:51

Heather Z.

Felicia S.

00:33

Dungarsinh P.

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Okay, so this is sort of a related rates like problem. Okay. But we can actually use the multi variable chain rule to sort of set it up in a nice way. So the first thing we need to remember is Okay, Well, what in the world is the volume of a right circular cone? Well, you can look it up. Or just believe me that the volume is one third. The base of the right circular cones is gonna be a circle, so pie r squared and then times the height each. And now what we know here is the d r d t is radius increases by three inches per second. So three and the D H D t is going to be to the height increases by two inches per second. And so we want to know DVT. But the chain rule says the D V d t is partial r mhm. Sorry. Partial B partial R d r d t plus partial v partial each times D h t t. Okay, So what's partial v partial are Well, that's just gonna be two thirds pi are h and then d r d t is three partial V partial h is one third pie r squared times D h t t. Which is to Okay, now we just want to plug in three for our in 12 for H. We'll have two thirds pi times three times 12 plus another three plus one third pi times three squared types too. And so what do we have? We have two times 36 times 12. 72. This is just going to be three times to, So it looks like 78. Hi. In our units will be inches cubed hermit.

Multivariable Optimization

Multiple Integrals

Vector Calculus