Question: Estimate (iint_{mathcal{S}} mathbf{F} cdot d mathbf{S}), where (mathcal{S}) is a tiny oriented surface of area 0.05 and the value of (mathbf{F}) at a sample point

Estimate $\iint_{\mathcal{S}} \mathbf{F} \cdot d \mathbf{S}$, where $\mathcal{S}$ is a tiny oriented surface of area 0.05 and the value of $\mathbf{F}$ at a sample point

Step by Step Solution

★★★★★

3.41 Rating (170 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Since S is a tiny surface we may assume that the dot product mathbfF cd... 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!

Sorenson Corp.s expected year-end dividend is D1 = $1.60, its required return is rs = 11.00%, its dividend yield is 6.00%, and its growth rate is expected to be constant in the future. What is...

Invert the following matrix over Z15 or prove that it cannot be inverted. 201 3 79 476

A random sample of data was collected on residential sales in a large city. The following table shows the sales price Y (in $ 1,000s), area X1 (in hundreds of square feet), number of bedrooms X2,...

The vector surface integral $\iint_{\mathcal{S}} \mathbf{F} \cdot d \mathbf{S}$ is equal to the scalar surface integral of the function (choose the correct answer): (a) $\|\mathbf{F}\|$. (b)...

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 $\mathbf{F}=\left\langle y,-x, x^{2}+y^{2}ightangle$, 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 $\mathcal{S}$...

$\iint_{\mathcal{S}} \mathbf{F} \cdot d \mathbf{S}$ is zero if (choose the correct answer): (a) $\mathbf{F}$ is tangent to $\mathcal{S}$ at every point. (b) $\mathbf{F}$ is perpendicular to...

Compute $\iint_{\mathcal{S}} \mathbf{F} \cdot d \mathbf{S}$ for the given oriented surface or parametrized surface. \(\mathbf{F}(x, y, z)=\langle-y, z,-xangle, \quad \Phi(u, v)=(u+3 v, v-2 u, 2...

Compute $\iint_{\mathcal{S}} \mathbf{F} \cdot d \mathbf{S}$ for the given oriented surface. $\mathbf{F}=y^{2} \mathbf{i}+2 \mathbf{j}-x \mathbf{k}$, portion of the plane $x+y+z=1$ in the octant...

Compute $\iint_{\mathcal{S}} \mathbf{F} \cdot d \mathbf{S}$ for the given oriented surface. $\mathbf{F}=\left\langle x, y, e^{z}ightangle$, cylinder $x^{2}+y^{2}=4,1 \leq z \leq 5$,...

Oceano T-Shirt Company sells a variety of T-shirts. Oceano presents the following data for its first two years of operations, 2012 and 2013. For simplicity, assume that all purchasing and selling...

Explain the assumptions underlying cost-volume-profit (CVP) analysis.

The following data were collected by Allegro Company for the month of March: Static budget data: \ table [ [ Sales , 9 , 0 0 0 units 0 $ 3 0 ? unit ] , [ Unit variable cost,$ 2 3 per unit ] , [ Total...

What range of measures are reported by your DMO to monitor organisation performance?

A tank is full of water. Find the work required to pump the water out of the spout. In Exercises 25 and 26 use the fact that water weighs 62.5 lb/ft 3 . 3 m

Solve Exercise 24 if the tank is half full of oil that has a density of 900 kg/m 3 .

What index is the first element of an atomic vector in R given? ( That is , at what index does R start counting? )

Plata Company produces two products: a mostly handcrafted soft leather briefcase sold under the label Maletin Elegant and a leather briefcase produced largely through automation and sold under the...

40 50 60 7 Conversion cost is the combination of direct labor cost and factory overhead cost. True False