1. Let 7(t) = < t³ – 2t², tet-t, 2t >. a. Find the unit tangent vector at t = 4. b. Write an equation for the tangent line at t = 4.

Q: sin t 1 8). du

A:

Q: Let y = 5 -5 and x = t – e'. Find any points which have a horizontal or vertical tangent line.

A: The parametric curve has a horizontal tangent if dydt=0;dxdt≠0 and vertical tangent if dxdt=0;dydt≠0

Q: Find the coordinates of the point where the equation y' – xy = 2 has a vertical tangent.

A:

Q: Find an equation of the tangent line to f(x) = x² at the point (3,9).

A:

Q: 5. Find the equation of the line (in Cartesian coordinates) tangent to r = 1– sine at the point (5).

A:

Q: b) Find the derivative of ľ 1 et In ydy.

A:

Q: x² + 1 Find the tangent line of y = at r = 1

A:

Q: Determine the equation of the line tangent to y = x + tan x at the point (T, T).

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.