Question

A space curve C is parametrically parametrically defined by x(t)=e^t^(2) −10, y(t)=2t^(3/2) +10, z(t)=−π, t∈[0,+∞). (a)...

A space curve C is parametrically parametrically defined by

x(t)=e^t^(2) −10,

y(t)=2t^(3/2) +10,

z(t)=−π,

t∈[0,+∞).

(a) What is the vector representation r⃗(t) for C ?

(b) Is C a smooth curve? Justify your answer.

(c) Find a unit tangent vector to C .

(d) Let the vector-valued function v⃗ be defined by

v⃗(t)=dr⃗(t)/dt

Evaluate the following indefinite integral

∫(v⃗(t)×i^)dt. (cross product)

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