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Mathematics LibreTexts

9.4: Tangent Planes and Linear Approximations

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  1. Find a vector tangent to the curve x2+xy+y2=3 at point P(1,1).
     
  2. Find a vector tangent to the curve (x2+y2)2=9(x2y2) at point P(2,1).
     
  3. Find a vector tangent to the curve 2x3x2y2=3xy7 at point P(1,2).
     
  4. Find the equation for the plane tangent to the surface 8x3y7z=19 at P(1,1,2).
     
  5. Find the equation for the plane tangent to the surface z=9x23y2 at P(2,1,39).
     
  6. Find the equation for the plane tangent to the surface x2+10xyz+y2+8z2=0 at P(1,1,1).
     
  7. Find the equation for the plane tangent to the surface z=ln(10x2+2y2+1) at P(0,0,0).
     
  8. Find the equation for the plane tangent to the surface z=e7x2+4y2 at P(0,0,1).
     
  9. Find the equation for the plane tangent to the surface xy+yz+zx=11 at P(1,2,3).
     
  10. Find the equation for the plane tangent to the surface z=sinx+siny+sin(x+y) at P(0,0,0).
     
  11. Find the equation for the plane tangent to the surface x2+y2+z2=1 at P(12,12,0).

9.4: Tangent Planes and Linear Approximations is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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