Find the unit tangent vector at the given value of t for the following parameterized curves. r(t)= ⟨7–√e^t,3e^t,3e^t⟩

, for 0≤t≤1
; t=ln 2

Step-by-step explanation:

Given :

We first have to differentiate of equation

Now to get a unit tangent vector at the given value of , we put in equation

                   [∵]

Now to get a unit tangent vector , we will divide our vector by its magnitude. So let's first find the magnitude.

Now we can find the our unit tangents vector.

Hence,

the answer is:

the answer is:

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!