(vi) Find the domain and the range of the function f(x, y) = 4√x² + y². Sketch the surface z = f(x, y) and the level curve f(x, y) -3. (CO3) [3]
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![(vi) Find the domain and the range of the function f(x, y)
Sketch the surface z = f(x,y) and the level curve f(x,y)
4 - √x² + y².
-3. (CO3) [3]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F55ae2c3d-db8a-4868-8838-b7d4cd87465a%2F9a39cd46-d776-4a3f-90b2-5bf654b5857c%2Fitfwju_processed.png&w=3840&q=75)
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- Find the slopes of the surface in the x- and y-directions at the given point.h(x, y) = x2 − y2(-2, 1, 3)The slope of the surface z = xy2 in the x-direction at the point (2,3) is ______, and the slope of this surface in the y-direction at the point (2,3) is ______. What are the answers?Verify Stoke's Theorem for F =( x²)i +(xz)j + (xyz)k and C is the curve of intersection betweenz=1 and z² = x² + y²
- Find a function f(x,y,z) whose level surface f=8 is the graph of the function g(x,y)=6x+7y f(x,y,z) = ?5. Find the area bounded by the parabolas y2=4x and y2+12x=36 6. Find the area bounded by the curve y=4x-x2and the lines x=-2 and y=4 7. Find the area bounded by the functions y=3x-x3and line y=2 8. Find the area in the first quadrant bounded by the curve x2y=a3and the lines x=2a, y=4a, and the axes.7. Graph the surface z = f (x, y) = x ^ 2 + 2 y ^ 2 - 2x + 4y + 2. Also write the reduced equation of the intersection curve of the surface with the z = 0 plane.
- The plane x = 1 intersects the paraboloid z = x2 + y2 in a parabola. Find the slope of the tangent line to the parabola at (1, 2, 5)A-) Find the equation of tangent plane to the surface x^2 + 2y^2 + 3z^2 = 21 which is parallel to the plane 2x + 4y + 6z = 3. B-)Find the extremum and saddle points of the function f (x, y) = x^3 − 3xy + y^3 if any.Find an equation for the level surface of the function f (x, y) = ln (x² + y²+ z²) that passes through the point (−1,2,1).
- 1) Find the area of the surface generated by rotating the function y=x^3 about the x-axis over 0≤x≤3 2) Find the area of the surface generated by rotating the function g(y) = (9-y^2) ^1/2 about the y-axis over 0≤y≤2.1. Consider the surface defined by z = x2 + e9y ln(x-y). Let f(x,y) = x2 + e9y ln(x-y). ○ Compute ∇f at the point (1,0). ○ Compute the derivative of f(x,y) at the point (1,0) in the direction (3,-4). ○ Explain the geometric relationship between the answer found in part (a) and the surface defined above.Tangents are drawn to x\power{2}+y\power{2}=1 from any arbitrary point P on the line 2x+y-4=0.The corresponding chord of contact passes through a fixed point whose coordinates are a. (1/4,1/2)b. (1/2,1) c. (1/2,1/4) d. (1,1/2)