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Find parametric equations for the line tangent to the curve of the intersection of the surfaces 3 2 2 3 x +/x y +y -8xy -Z" = 0 and x +y Aw- + 2" =3 at the point P(1, 1,1). Select the parametric equations for the tangent line. O A. x= 9t O B. x=1-22t y= 1 - 9t y = 1+ 22t Z = 1 Z = 1 O C. x= 1+22t O D. x= 1+9t y = 1 - 22t V= 1 - 9t Z = 1 Z = 1+9tFind parametric equations for the line tangent to the curve of the intersection of the surfaces 3 + y' - 8xy - z" = 0 and x " +y + z =3 at the point P(1, 1, 1). Select the parametric equations for the tangent line. O A. x=9t O B. x=1- 22t y= 1 - 9t Z = 1 y = 1+ 22t Z = 1 O C. x=1+22t O D. x = 1+9t y =1 - 22t V= 1 - 9t Z =1 Z = 1+ 9tFind the linearization L(x,y) of the function f(x,y) = 9x - 5y + 9 at the points (0,0) and (1,1). The linearization of f(x y) at (0,0) is 9+ 9x - 5y. The linearization of f(x.y) at (1, 1) isFind the linearization L(x,y) of the function f(x,y) =x- -7xy +7 at Po (4,4). Then find an upper bound for the magnitude |E of the error in the approximation f(x.y) ~ L(x.y) over the rectangle R: |x - 4| $0.4, ly - 4| = 0.4. The linearization of f is L(x,y) =Find the linearization L(x,y,z) of the function f(x,y,z) at the given points. f(x,y,z) =e*+ cos (y+ z) C. 0, 4 14 b. 0,I, a. (0,0,0)Suppose that T is to be found from the formula T=y(e*+ e *), where x and y are found to be In 2 and 2 with maximum possible errors of |dx = 0.05 and dy| =0.1. Estimate the maximum possible error in the computed value of T. The magnitude of the estimated maximum possible error is (Type an integer or a decimal.)Suppose thatT is to be found from the formula T =1,r( ex + a _x], where x and 3r are found to be In 2 and 2 with maximum possible errors of |d::-:| = [1.05 and |dy| = 111. Estimate the maximum possible error in the computed value of T. The magnitude of the estimated maximum possible error is E. [Type an integer or a decimal.) A smooth curve is tangent to a surface f(x,y,z) = c at a point of intersection if the curve's velocity vector is orthogonal to Vf at the point. Show that the curve r(t) = 2vti+ 2vtj+ (8t -6)k is tangent to the surface x" +y- -z =6 when t= 1.One can show that these two vectors are orthogonal at the point of intersection, (). by showing that their is equal to (Type exact answers.) What is the formula for Vf? Vf= Find Vf for the given surface. vf = (+ + ()+() Now find the gradient vector at the point of intersection. Find the curve's velocity vector. v(1) = )++ ();+(OK Evaluate the curve's velocity vector at t = 4. v(4) = (D+ (D)+ ()* (Simplify your answers.) Because the of the velocity vector of r(t) and the gradient vector at t = 4 is , it follows that the curve r(t) = 3vti + 3vt] + (18t-66)k is tangent to the surface x + y- -z = 66 when t = 4.Consider a closed rectangular box with a square base, as shown in the figure. Assume x is measured with an error of at most 0.6% and y is measured with an error of at most 0.70%, so we have