Problem 1) Let T (t) represent the unit tangent vector of 7(t) = < 1,t, t² >. A student is asked to calculate T '(0). The student starts by finding i '(t) =< 0,1,2t >. Plugging in t = 0, they find 7 '(0) =< 0,1,0 >. This is already a unit vector, so they conclude that T(0) =< 0,1,0 >. Finally, to find T '(0), they take the derivative of < 0,1,0 > component-wise. They conclude that T'(0) =< 0,0,0 >. The student's answer is incorrect. What mistake did the student make?

Q: Find equation of the tangent line to the curve y = v2x + 1 at the point (4,3).

A: Given:    y = √(2x+1)  Point (4,3)

Q: 5. Find the equation of the tangent line for: x = vt + 9, y= at (4,-)

A: The objective is to find the equation of the tangent line.

Q: 3) Find an equation of the tangent line to the graph of y = (z + 4)² at z = 4.

A:

Q: Find the first, second, and third derivatives of the func- tion. W (t) = 5t² + 4e*.

A: NOTE: Refresh your page if you can't see any equations. . take the first derivative…

Q: 10) Find the tangent line to the curve 16 1 at the point (4 23).

A:

Q: 2.x²y+ 3xy? = 2x + 55

A: We will find the value of dy/dx and the equation of the tangent line at point (5,1) in the following…

Q: Find the velocity and acceleration vectors and the equation of the tangent line for the curve r(t) =…

A:

Q: Find the derivative of r(t)=(5-1³) î+2te¹¹ ĵ+sin 31 k and find the unit tangent vector at the point…

A:

Q: Find the velocity and acceleration vectors and the equation of the tangent line for the curve r(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.