Consider the following parametric equations: x= √t y=√(t−1) (a) Sketch the curve represented by the parametric equations. Be sure to indicate the orientation. Find dy/dx (b) Find the exact value of the slope of the tangent line to the curve at the point t = 3. c) Find d^2y/dx^2 d) Determine the concavity of the plane curve at the point t = 3
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.
Consider the following parametric equations:
x= √t
y=√(t−1)
(a) Sketch the curve represented by the parametric equations. Be sure to indicate the orientation. Find dy/dx
(b) Find the exact value of the slope of the tangent line to the curve at the point t = 3.
c) Find d^2y/dx^2
d) Determine the concavity of the plane curve at the point t = 3
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