Answer :
The length of the trajectory of the function f(t) = (2t , 1, [tex]e^{2} + e^{-t}[/tex]) is 3/2
Calculation
length = [tex]\int\limits^b_a {\sqrt{(\frac{dx}{dt})^2 + (\frac{dy}{dt})^2 + (\frac{df}{dt})^2 } \, dx[/tex]
=[tex]\int\limits^{ln2}_0 {e^{t}+ e\\^{-t} } \, dt[/tex]
=(2+1) - (1/2+1)
=2-1/2 =3/2
What is a vector?
In mathematics and physics, the term “vector” is used informally to describe certain quantities that cannot be described by a single number or by a set of vector space elements.
A vector example is what?
A quantity or phenomena with independent qualities for both magnitude and direction is called a vector. The term can also refer to a quantity’s mathematical or geometrical representation.
Velocity, momentum, force, electromagnetic fields, and weight are a few examples of vectors in nature.
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