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Chapter 11: Q. 44 (page 860)

Evaluate the limits in Exercises 42鈥�45.

limt鈫�1-(lnt,et-1t-1,et)

Short Answer

Expert verified

The evaluation of the limit limt鈫�1-(lnt,et-1t-1,et)is (0,e,e).

Step by step solution

01

Step 1. Given Information.

The function:

limt鈫�1-(lnt,et-1t-1,et)

02

Step 2. Apply the limits.

By applying the limit and solving,

limt鈫�1-(lnt,et-1t-1,et)=limt鈫�1-(lnt)i+limt鈫�1-(et-1t-1)j+limt鈫�1-etk=(ln1)i+e1j+e1k=0i+ej+ek=(0,e,e)

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Most popular questions from this chapter

Explain why the graph of every vector-valued function r(t)=cost,sint,f(t)lies on the surface of the cylinder x2+y2=1for every continuous functionf.

For each of the vector-valued functions in Exercises , find the unit tangent vector and the principal unit normal vector at the specified value of t.

rt=cos伪t,sin伪t,where伪>0,t=蟺

Lett=f(蟿)beadifferentiablereal-valuedfunctionof蟿,andletr(t)beadifferentiablevectorfunctionwitheithertwoorthreecomponentssuchthatf(蟿)isinthedomainofrforeveryvalueof蟿onsomeintervalI.Finddrf蟿d蟿.

For each of the vector-valued functions in Exercises, find the unit tangent vector and the principal unit normal vector at the specified value of t.

rt=sin2t,cos2t,t,t=蟺4

For each of the vector-valued functions in Exercises 22鈥�28, find the unit tangent vector.

r(t)=(cos3t,sin3t)
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