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Calculus & Its Applications (14th Edition)
- Let f (x, y) and g(x, y) be functions of two variables withthe property that ∂ f/∂x= ∂g/∂x and ∂ f/∂y= ∂g/∂y for every point(x, y) ∈ R2. What is the relationship between f and g?arrow_forwardq2) Let f(x,y,z) be a function that satisfies fx(1,-2,3)=1, fy(1,-2,3)=-3 and fz(1,-2,3)=2. What is the value of the directional derivative Duf(1,-2,3) where u=4i+3k ? a. 2 b. 10 c. 0 d. -5arrow_forwardLet f(x.y.z) be a function that satisfies fx(1,-2,3)=1, fy(1,-2.3)=-3 and f,(1,-2,3)=2. What is the value of the directional derivative Duf(1,-2,3) where u=4i+3k ? а. 2 O b. 10 O.O O d.-5arrow_forward
- Let f(x.y.z) be a function that satisfies fx(1,-2,3)=1, fy(1,-2.3)=-3 and f-(1,-2,3)=2. What is the value of the directional derivative Duf(1,-2,3) where u=4i+3k ? а. 10 O b.-5 OC. 2 O d.0arrow_forwardLet f(x.y.z) be a function that satisfies fx(1,-2,3)=1, fy(1,-2.3)=-3 and f-(1,-2,3)=2. What is the value of the directional derivative Duf(1,-2.3) where u=4i+3k ? O a. 2 Ob. 10 O.O O d.-5arrow_forwardLet f: R² → R be defined by f(x, y) = 3x¹ + 7y³ +7 and set z = f(x, y). Find an equation for the contour line (level set) of f at level z= 9. help (equations)arrow_forward
- Evaluate AF du at (u, v)=(5,5) for the function w(x,y) = 2y-y²; du x=U-V иб , учиarrow_forwardFind the domain of f (x, y) = x + Yarrow_forwardSuppose that f(x, y) = -2z4+3 zy2 + 3y2, z=rcos (t) and y=rsin(t). Find af af and (write your answers as functions of the pair r and t). Ot Or af Or af ICHarrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage