3-12 Find an equation for the tangent plane and parametric equations for the normal line to the surface at the point P. 4. x'y - 422 = -7; P(-3, 1, -2)
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- (a) Find an equation of the tangent plane to the surface at the given point. x2 + y2 + z2 = 14, (1, 3, 2) (b) Find a set of symmetric equations for the normal line to the surface at the given point.1- Maryam sits at the point on the curve y=(×+2)? where the normal to that curve is parallel to the y-axis. 2-The line tangent to a curve at a point (x1, y1) is y = 2x - 2. The normal to that curve at the same point passes through (11, -5). Titan sits at the point (x1, y1).Given the surface S: 2xy −3yz+z2=−5 and the point P: (1, 2, 3). (a) Find the equation of the tangent plane to S at P correctly. (b) Find the normal line to S at P correctly.
- Find the equation for the tangent plane to the surface at the indicated point. (Hint: Solve for z in terms of x and y.) z = e6x2 + 8y2, P(0, 0, 1)3. The curve y =ax2 +bx +c passes through the point (2, 4) and is tangent to the line y = x + 1 at (0, 1). Determine values for a, b, and c. Gauss sits at the point (-b –c, 4a).Consider the following. x = sin(6t), y = −cos(6t), z = 24t; (0, 1, 4?) (a) Find the equation of the normal plane of the curve at the given point. (b)Find the equation of the osculating plane of the curve at the given point.
- Consider the following. x = sin(6t), y = −cos(6t), z = 24t, (0, 1, 4?) Find the equation of the normal plane of the curve at the given point. Find the equation of the osculating plane of the curve at the given point.Consider the curve C shown in the accompanying figure, which is the intersection between surfaces S1 and S2, with S1: z = a2 - x2 and S2: x + y + z = a2 + a, for a> 1. The figure is in the first attached image A parameterization of curve C is: The answers are in the second attached imagea) Find the equation of the normal plane at t=0 b) Find the equation of the osculating plane at t=0
- Consider the surface S: z = 3x2 + 3y2. An equation of the plane tangent to S at the point P (2, −2, 24) is given by: Answers in the picture:Find the equation of the curve at any point P(x,y) of a curve the subtangent equals -1/xWhich of the following regions have the same area?I. The region enclosed by the curve y = |x2 − 1|, the lines x = 0 and x = 2, and the x-axis.II. The region enclosed by the curve y=x3- 4x2+6x and its tangent line at the point x = 1.III. The region enclosed by the curves x2 = 4y and y =8/(x2 + 4).IV. The region enclosed by the curve y = x*ln(x) and the line y = x2.V. The region between the curve y =1√x, x-axis, and the lines x = 1 and x=4. Which one of the following answer is true? (a) I, II, III(b) I, V(c) II, III, IV(d) II, IV(e) III, IV