9.4: Tangent Planes and Linear Approximations
( \newcommand{\kernel}{\mathrm{null}\,}\)
- Find a vector tangent to the curve x2+xy+y2=3 at point P(−1,−1).
- Find a vector tangent to the curve (x2+y2)2=9(x2−y2) at point P(√2,1).
- Find a vector tangent to the curve 2x3−x2y2=3x−y−7 at point P(1,−2).
- Find the equation for the plane tangent to the surface −8x−3y−7z=−19 at P(1,−1,2).
- Find the equation for the plane tangent to the surface z=−9x2−3y2 at P(2,1,−39).
- Find the equation for the plane tangent to the surface x2+10xyz+y2+8z2=0 at P(−1,−1,−1).
- Find the equation for the plane tangent to the surface z=ln(10x2+2y2+1) at P(0,0,0).
- Find the equation for the plane tangent to the surface z=e7x2+4y2 at P(0,0,1).
- Find the equation for the plane tangent to the surface xy+yz+zx=11 at P(1,2,3).
- Find the equation for the plane tangent to the surface z=sinx+siny+sin(x+y) at P(0,0,0).
- Find the equation for the plane tangent to the surface x2+y2+z2=1 at P(1√2,1√2,0).