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3 years ago

While in college, why did Euler work through advanced math books on his own

Mathematics

2 answers:

gavmur [86]3 years ago

8 0

His teacher didnt have time so advised him to tutor privately

Papessa [141]3 years ago

7 0

Answer:

Professor Johann Bernoulli was a very busy person, and refused to give Euler private lessons.

Step-by-step explanation:

Johann Bernoulli would not teach Leonhard Euler privately, mainly on superficial math problems.

But Euler received from Johann Bernoulli a valuable advice to read more advanced math books on his own and work on more elaborated problems, and only if he could not be able to solve a equation he was allowed to visit Johan on Sunday afternoon to help him.

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G find the area of the surface over the given region. use a computer algebra system to verify your results. the sphere r(u,v) =

Svetach [21]

Presumably you should be doing this using calculus methods, namely computing the surface integral along $\mathbf r(u,v)$ .

But since $\mathbf r(u,v)$ describes a sphere, we can simply recall that the surface area of a sphere of radius $a$ is $4\pi a^2$ .

In calculus terms, we would first find an expression for the surface element, which is given by

$\displaystyle\iint_S\mathrm dS=\iint_S\left\|\frac{\partial\mathbf r}{\partial u}\times\frac{\partial\mathbf r}{\partial v}\right\|\,\mathrm du\,\mathrm dv$

$\dfrac{\partial\mathbf r}{\partial u}=a\cos u\cos v\,\mathbf i+a\cos u\sin v\,\mathbf j-a\sin u\,\mathbf k$
$\dfrac{\partial\mathbf r}{\partial v}=-a\sin u\sin v\,\mathbf i+a\sin u\cos v\,\mathbf j$
$\implies\dfrac{\partial\mathbf r}{\partial u}\times\dfrac{\partial\mathbf r}{\partial v}=a^2\sin^2u\cos v\,\mathbf i+a^2\sin^2u\sin v\,\mathbf j+a^2\sin u\cos u\,\mathbf k$
$\implies\left\|\dfrac{\partial\mathbf r}{\partial u}\times\dfrac{\partial\mathbf r}{\partial v}\right\|=a^2\sin u$

So the area of the surface is

$\displaystyle\iint_S\mathrm dS=\int_{u=0}^{u=\pi}\int_{v=0}^{v=2\pi}a^2\sin u\,\mathrm dv\,\mathrm du=2\pi a^2\int_{u=0}^{u=\pi}\sin u$
$=-2\pi a^2(\cos\pi-\cos 0)$
$=-2\pi a^2(-1-1)$
$=4\pi a^2$

as expected.

6 0

3 years ago

What’s the LCD Of 5/8

77julia77 [94]

There isnt a way the LCD can go lower, because 5 only counts by 5's and 5 and 8 meet at 40.

6 0

3 years ago

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Pls help me aim stuck on this

KIM [24]

D it's store d, it's the cheapest

3 0

3 years ago

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Una carretera recta tiene un ángulo de elevación de 3 grados respecto al plano horizontal. ¿Qué distancia hay que recorrer para

geniusboy [140]

Answer:

572.4 m

Step-by-step explanation:

Fórmula del ángulo de elevación =

tan θ = Opuesto / Adyacente

θ = 3 °

Opuesto = 30 m

Adyacente =?

Por eso

bronceado 3 = 30 m / x

Multiplicar cruzada

bronceado 3 × x = 30 m

x = 30 m / bronceado 3

x = 572.43410063m

Aproximadamente = 572.4 m

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2 years ago

What makes the shapes similar?

son4ous [18]

Answer:

The answer is the first option

hope this helps

Step-by-step explanation:

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3 years ago