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Chapter 11: Q. 40 (page 902)

Find the equation of the osculating circle to the given scalar function at the specified point.

f(x)=ln⁡x,(1,0)

Short Answer

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Step by step solution

01

Step 1. Given information.

given,

f(x)=ln⁡x,(1,0)

02

Step 2. 

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Most popular questions from this chapter

Let C be the graph of a vector-valued function r. The plane determined by the vectors T(t0) and B(t0) and containing the point r(t0) is called the rectifying plane for C at r(t0). Find the equation of the rectifying plane to the helix determined by r(t)=(cost,sint,t)when t = π.

Evaluate the limits in Exercises 42–45.

limt→0(sin3t,cos3t)

Every description of the DNA molecule says that the strands of the helices run in opposite directions. This is meant as a statement about chemistry, not about the geometric shape of the double helix. Consider two helices

h1(t)=⟨cos⁡t,sin⁡t,αt⟩andh2(t)=⟨sin⁡t,cos⁡t,αt⟩

(a) Sketch these two helices in the same coordinate system, and show that they run geometrically in different directions.

(b) Explain why it is impossible for these two helices to fail to intersect, and hence why they could not form a configuration for DNA.

Explain why the graph of every vector-valued function r(t)=cost,sint,costlies on the intersection of the two cylinders x2+y2=1andy2+z2=1.

Find parametric equations for each of the vector-valued functions in Exercises 26–34, and sketch the graphs of the functions, indicating the direction for increasing values of t.

r(t)=(tsint,tcost,t)fort∈[0,4π]
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