calculus

how do I find the range of a natural log like
ln | x/(1+x^2) |

  1. 👍 0
  2. 👎 0
  3. 👁 119
  1. Consider the function
    u = │x/(1+x^2)│

    it looks like birdwings, with (0,0) a cusp, the curve rising to a maximum of (1,1/2) and then dropping again to approach the x-axis with the x-axis as an asymptote. It is symmetric about the y-axis.

    so then you are looking at ln u

    u lies between 0 and 1/2 , so ln u will always be negative.

    ln 1/2 = -.693 and for all other of u values which will be less than 1/2 ln u will be less than -.693

    as u --> 0 ln u approaches negative infinity

    so the range is ≤ -.693

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Exponents-word problem

    A culture starts at 8600 bacteria. After one hour the count is 10,000. Find a function that models the number of bacteria n(t) after t hours. The answer is n(t) = 8600e^.1506t Where does this 0.1506 come from? Thanks. n(t) = 8600

  2. Math

    If ln a=2, ln b=3, and ln c=5, evaluate the following: (a) ln(a^−2/b^4c^−3)= -.9524 (b) ln(√b^−4*c^1*a^−1)= -1.739 (c) ln(a^2b^4)/ln(bc)^−2= 42.39 (d) (ln(c^−1))*(ln(a/b^3))^−4= -.03507 I am getting these answers

  3. Chemistry

    How do you do the inverse of absolute temperature? My kelvin temperatures are: 298 308 318 328 338 348 358 368 378 Taking the natural log of both sides of both sides of the equation gives ln(k) = ln(A) – E/RT. Thus, a graph of

  4. Algebra 2

    How is the expression log 32 - log 8 written as a single logarithm? log 4 log 8 log 24 log 40

  1. Logarithms

    1. Find the amount of time required for an investment to double at a rate of 12.3% if the interest is compounded continuously. MY ANSWER: 5.635 yrs 2. Solve e^(0.2x) < 21.2 by using natural logarithms. MY ANSWER: X

  2. Trigonometry

    This is a logs question If u=x/y^2, which expression is equivalent to log u? 1) log x + 2 log y 2) 2(log x- log y) 3) 2(log x + log y) 4) log x- 2 log y

  3. chem

    this is my question Calculate the hydronium ion consentration and the hydroxide concentration in blood in which the PH is 7.3. I don't have invlog on my calculator so I hit log(7.3)= .863 for hydronium. Is this dumb for me to do?

  4. Trigonometry

    The expression log(x^n/ radical y)is equivalent to 1. n log x - 1/2 log y 2. n log x- 2 log y 3. log (nx) - log (1/2y) 4. log (nx) - log (2y)

  1. precalc

    Suppose that u=log(2) and v=log(5). Find possible formulas for the following expressions in terms of u and/or v. Your answers should NOT involve any log's. a) log(0.4)= b) log(0.08)= c) log(2500)=

  2. math(Please help)

    1) use the properties of logarithms to simplify the logarithmic expression. log base 10 (9/300) log - log 300 log 9 = 2 log 3 log 300 = log 3 + log 100 = log 3+2 I just do not know how to put these together now!

  3. math

    Calculate without using tables or calculators log 450 and log 324 given log 2 =0.3010 and log 3 =0.4771

  4. Mathematics

    Prove that log a, log ar, log ar^2 is an a.p. Is the following below correct? Log ar^2 - Log ar= Log ar - Log a hence applying laws of logarithm Log(ar^2/ar) = log(ar/a) Log and log cancels out and then cross-multiply hence a^2r^2

You can view more similar questions or ask a new question.