   Chapter 12.4, Problem 35E

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# Sketching a Graph and Vectors In Exercises 21-24, sketch the graph or the plane curse r( t) and sketch the sectors T( t) and T( t) at the given value of t r ( t ) = ( 2 t + 1 ) i − t 2 j , t = 2

To determine

To Graph: Sketch the graph of r(t), T(t), N(t) at the given of t.

Explanation

Given: r(t)=(2t+1) it2j,   t=2

Graph:

Using desmo graphing calculator required graph is

Using desmo graphing calculator required graph of unit normal vector and unit tangent vector will be

Interpretation:

Position vector given is:

r(t)=(2t+1) it2j, t=2

from above equation, we can obtain vector value of function

x=2t+1y=t2y=(x12)2(x1)2+2y=0

xy=1 is a rectangular equation for given vector valued function.

By using Desmo graphing calculator graph is plotted.

The derivative of r(t) is given as

r'(t)=ddt(r(t))=ddt((2t1) i^t2j^)=2i^2tj^

r'(t)=(1)2+(3t2)2=(2)2+(2t)2=21+t2

Unit tangent vector is given as

T(t)=r'(t)r'(t)2i^2tj^21+<

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