The curvature of the curve a(t) = 2te₁ + (1 − t²)e₂ − 3te3 at the point (2,0,-3) is

Q: Find the equation of the tangent plane to the surface z = 4x² + 7y² + 9xy at the point (1, -2, 14).…

A:

Q: Calculate the length of the curve F (t) = (2t-1, t + 1) with t ∈ [1,2].

A: Given that  the curve F (t) = (2t-1, t + 1) with t ∈ [1,2]. To Calculate the length of the curve in…

Q: For the following two parts, the curve C is the part of y = 4 - a² from (0, 4) to (2,0). (a)…

A:

Q: Find an equation of the tangent plane to the surface z = -2z² – 2y?- lz 2y+ 3 at the point (5, 1,…

A:

Q: Evaluate √(2² + yz sin(xyz))dx+(y²+xz sin(xyz))dy+(x+xysin(xyz))dz where C is the curve following…

A:

Q: Find the equation of the tangent plane to z = e* + y + y° +1 at the point (0, 4, 70).

A:

Q: Q. (a) Find an equation of the tangent plane to each surface at the given point. (b) Find symmetric…

A:

Q: Find the equation of the tangent line to the common curve of the two surfaces with equations z = x²…

A: Please check step 2 for solution.

Q: A car travels over the hill having the shape of a parabola. When the car is at point A, it is…

A:

Q: Find the curvature and the radius of curvature of the curve y = x + 5x2 – 2x3 at the origin (0,0).

A:

Q: Sketch the two curves 7(t) = tî + t²j; t e [1, 5] and B(T) = e"î + e²r3; T E [0, In 5]. How are they…

A:

Q: Sketch the curve r(t)=f°i+tj and indicate the orientation. Find r'(t) and sketch r(1) & r°(1).

A: First we will plot the given parameters.

Q: Given the function z = In(x - 2y), find the equation of the tangent plane when (x, y) = (3, 1) in…

A:

Q: Consider the tangent line to the curve r(t) = t2i −(1/(t + 1))j +(4 − t2)k at the point P(4, 1, 0).…

A: Given the tangent line to the curve r→t=t2i^−1t+1j^+4−t2k^  at the point P4,1,0. We have to…

Q: Find the equation of the tangent plane to z = e² + y + y² +8 at the point (0, 4, 269). Z= 0

A:

Q: Determine the intersection point of the lines tangent to the curve r (t) = (senπt, 2senπt, cosπt) at…

A: The given curve is rt=sinπt,2sinπt,cosπt. Differentiating it with respect to t:…

Q: Find the equation of the tangent plane to the graph of the curve f(x, y) = x² + y² at the point…

A:

Q: Find an equation of the tangent plane to the surface z = 2y² – 3x² at the point (-3, -3, -9).

A:

Q: Find all values of t for which the curve given parametrically by x(t) = 4+ 2t2 y(t) = 212 + t3 , is…

A: Explained below

Q: Find for the curve dx In (2x) + 5xy + y = 3.

A:

Q: Find the equation of normal to the hyperbola        x2 -9y2=7 At the point (4,1).

A: