Using Stoke’s Theorem In Exercises 7-16, use Stoke’s Theorem to evaluate
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Calculus (MindTap Course List)
- Using the Midpoint Formula Use the result of Exercise 53 to find the endpoint (x2,y2) of each line segment with the given endpoint (x1,y1) and midpoint (xm,ym). ax1,y1=1,2xm,ym=4,1bx1,y1=5,11xm,ym=2,4arrow_forwardSketch the plane curve represented by the vector valued function and give the orientation of the curve. r(t) = (t2 + t)i + (t2 − t)jarrow_forwardDefinition 3.32 If f is a function of two variables x and y such that f. and fy exist, then the gradient of f, denoted by Vƒ (read as “del f"), is given by V{(r,y) = f.(z. y) i + f,(r, y) j. Note that the gradient Vf(x, y) is a vector and Df(1,9) = U - V j(z, y). Suppose a is the radian measure of the angle between U and Vf. Then D7f(z, y) = U·Vf(r, y) = ||U|||Vf(r, y)|| o a. (3.2) Equation (3.2) tells us that D#f(x, y) will be a maximum when cos a = 1; so that we have ||Vf(x, y)|| gives the maximum value of D7f at the point (r, y).arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageElementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning