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Chapter 11: Q. 43 (page 860)

Evaluate the limits in Exercises 42鈥�45.

limt鈫�蟺(sint,cost,sect)

Short Answer

Expert verified

The evaluation of the limit limt鈫�蟺(sint,cost,sect)is (0,-1,-1).

Step by step solution

01

Step 1. Given Information.

The function:

limt鈫�蟺(sint,cost,sect)

02

Step 2. Apply the limits.

By applying the limit and solving,

limt鈫�蟺(sint,cost,sect)=limt鈫�蟺(sint)i+limt鈫�蟺(cost)j+limt鈫�蟺(sect)k=蝉颈苍蟺i+肠辞蝉蟺j+sec蟺办=0i-j-k=(0,-1,-1)

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Most popular questions from this chapter

Let r(t)=x(t),y(t),z(t)be a differentiable vector function on some interval I鈯�Rsuch that the derivative of the unit tangent vector T(t0)=0, where t0鈭�I. Prove that the binormal vectorB(t0)=T(t0)脳N(t0)

(a) B(t0)is a unit vector;

(b)B(t0)is orthogonal to both T(t0)and N(t0).

Also, prove that T(t0),N(t0), and B(t0)form a right-handed coordinate system.

For constants 伪,尾, and 纬, the graph of a vector-valued function of the form

r(t)=伪e纬t(cost)i+伪e纬t(sint)j+尾e纬tk,t鈮�0

For each of the vector-valued functions, find the unit tangent vector.

r(t)=(t,t2,t3)

In Exercises 19鈥�21 sketch the graph of a vector-valued function r(t)=x(t),y(t) with the specified properties. Be sure to indicate the direction of increasing values oft.

Domainlocalid="1649578696830" t鈮�0,r0=0,3,r1=-2,1,limt鈫�鈭�x(t)=-5,andlimt鈫�鈭�y(t)=-鈭�.

Let r(t) be a differentiable vector function such that r(t)路r'(t)=0 for every value of t. Prove that 鈥�r(t)鈥� is a constant.
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