(a) Find the smallest positive number N such that for eachx in the interval (N , +), the

Chapter 1, Problem 39

(choose chapter or problem)

(a) Find the smallest positive number N such that for each x in the interval \((N,+\infty)\), the value of the function \(f(x)=1 / x^{2}\) is within 0.1 unit of \(L=0\)

(b) Find the smallest positive number N such that for each x in the interval \((N,+x)\), the value of \(f(x)=x /(x+1)\) is within 0.1 unit of \(L=1\) .

(c) Find the largest negative number N such that for each x in the interval \((-\infty, N)\), the value of the function \(f(x)=1 / x^{3}\) is within 0.001 unit of \(L=0\)

(d) Find the largest negative number N such that for each x in the interval \((-x, N)\), the value of the function \(f(x)=x /(x+1)\) is within 0.1 unit of \(L=1\)

Equation Transcription:

 

Text Transcription:

(N,+ infinity)

 f(x)=1/x^2

L=0

(N,+x)

f(x)=x/(x+1)

L=1

(-infinity ,N)

f(x)=1/x^3

(-x,N)

f(x)=x/(x+1)