Question: Let (mathcal{S}) be a small patch of surface with a parametrization (Phi(u, v)) for (0 leq u leq 0.1,0 leq v leq 0.1) such that

Let $\mathcal{S}$ be a small patch of surface with a parametrization $\Phi(u, v)$ for $0 \leq u \leq 0.1,0 \leq v \leq 0.1$ such that the normal vector $\mathbf{N}(u, v)$ for $(u, v)=(0,0)$ is $\mathbf{N}=\langle 2,-2,4angle$. Use Eq. (3) in Section 16.4 to estimate the surface area of $\mathcal{S}$.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

We use Eq 1 in Section 174 with leftui j vi jight00 mathcalRi jmathcalR001 times... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Calculus 4th Questions!

Let $\mathcal{S}$ be the surface with parametrization \[ \Phi(u, v)=\left(\left(1+v \cos \frac{u}{2}ight) \cos u,\left(1+v \cos \frac{u}{2}ight) \sin u, v \sin \frac{u}{2}ight) \] for \(0 \leq u...

The following additional information is available for the Dr. Ivan and Irene Incisor family from Chapters 1-5. Ivan's grandfather died and left a portfolio of municipal bonds. In 2012, they pay Ivan...

A flat coil of wire has an area A, N turns, and a resistance R. It is situated in a magnetic field, such that the normal to the coil is parallel to the magnetic field. The coil is then rotated...

EAS Let $\mathcal{S}$ be the surface with parametrization \[ \Phi(u, v)=((3+\sin v) \cos u,(3+\sin v) \sin u, v) \] for $0 \leq u \leq 2 \pi, 0 \leq v \leq 2 \pi$. Using a computer algebra...

Let $\mathbf{F}=\langle z, 0, yangle$, and let $\mathcal{S}$ be the oriented surface parametrized by $\Phi(u, v)=\left(u^{2}-v, u, v^{2}ight)$ for $0 \leq u \leq 2$, $-1 \leq v \leq 4$....

Let $\mathcal{S}$ be the surface parametrized by \[ \Phi(u, v)=\left(2 u \sin \frac{v}{2}, 2 u \cos \frac{v}{2}, 3 vight) \] for $0 \leq u \leq 1$ and $0 \leq v \leq 2 \pi$ (a) Calculate the...

Let $\mathcal{S}$ be the half-cylinder $x^{2}+y^{2}=1, x \geq 0,0 \leq z \leq 1$. Assume that $\mathbf{F}$ is a horizontal vector field (the $z$-component is zero) such that \(\mathbf{F}(0,...

Let $\mathcal{S}$ be the surface of the cylinder (not including the top and bottom) of radius 2 for $1 \leq z \leq 6$, oriented with outward-pointing normal (Figure 16). (a) Indicate with an...

Potential Due to a Uniform Sphere Let $\mathcal{S}$ be a hollow sphere of radius $R$ with its center at the origin with a uniform mass distribution of total mass $m$ [since $\mathcal{S}$ has...

Let $\mathbf{F}=\left\langle y,-x, x^{2}+y^{2}ightangle$, and let $\mathcal{S}$ be the portion of the paraboloid $z=x^{2}+y^{2}$ where $x^{2}+y^{2} \leq 3$. (a) Show that if $\mathcal{S}$...

Texas Oil owns a parcel of land that has the potential for containing much oil, some oil, or no oil underground. The company needs to decide whether or not to drill on this parcel. The payoffs are as...

Explain the collage regarding self representation in environment WELL BIODIVERSITY COLLAPSE CLIMATE CHANGE IN

Of these choices, a risk - adverse investor who prefers to minimize interest rate risk is most apt to invest in: Muttiple Choice 5 year, 7 percent coupon bonds. 2 0 year, zero coupon bonds. 2 0 yeac...

1. Divide into four- to six-person teams and do either A or B, depending on feasibility. A. Choose a production job at a fast-food restaurant and, after making appropriate modifications of the...

Determine whether each integral is convergent or divergent. Evaluate those that are convergent. 3 1 -dx -2 X x*

Determine whether each integral is convergent or divergent. Evaluate those that are convergent. dx /1 x

Determine whether each integral is convergent or divergent. Evaluate those that are convergent. 1 dx 1

1)Lattimer Company had the following results of operations for the past year: Sales (15,000 units at $11.85) $177,750 Variable manufacturing costs $95,250 Fixed manufacturing costs 18,750 Selling and...

Rev. Carla Fitzerald is a full time minister. The church allos her to use a parsonage that has an annual fair rental value of $26,000. The church pays her an annual salary of $69,000, of which $6,500...

Assume that you are the portfolio manager of the Delaware Fund, a $4 million mutual fund that contains the following stocks: Stock Amount Beta A $400,000 1.50 B $600,000 0.50 C $1,000,000 1.25...