Find parametric equations for the tangent line to the given curve at the point (30, 135, 469). The curve and the tangent line must have the same velocity vector at this point. x(1) = 12 + 6/i y(t) = 61312 – 3t z(t) = 512 + 7t +1 x(1) = y(t) = z(1) = | Give the unit tangent vector to the curve at (30, 135, 469) T = (

Q: #37) (modified) Find the equation if the tangent line at the point x=1: y = x4 + 1/x - 3ex

A:

Q: Consider the curve 6+2xy + y³ = 4 The equation of the tangent line to the curve at the point (1, 1)…

A:

Q: a) Find an equation for the tangent line to the curve y= 2/x at the point (2, 1) on this curve.

A:

Q: 1. a) Find dy for the equation 4x²y ² - x ³y = 3 dx b) find the x-coordinate of each point on the…

A:

Q: The equation below defines y implicitly as a function of x: 2x2 + xy = 3y2 Use the equation to…

A:

Q: Sketch the curve f(x, y) = c together with Vƒ and the tangent line at the given point. Then write an…

A: Curve sketch for 2x2 -y = 13 Curve sketch for  3xy = -54

Q: Find an equation of the line tangent to the curve defined by æ° + 2xy + y = 104 at the point (2, 2).…

A:

Q: (2.;v3). 1 Find the equation of the tangent line to x? +y²: = 1 at Use exact values in y = mx + b…

A:

Q: 1 - Find the equation of the tangent line to the curve y = 3 5 x2 +6x 2 11 at its point of…

A:

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.