Post a New Question

Linearization

posted by .

Find the linear approximation of the function f(x) = √16-x at a = 0

  • Linearization -

    What is a? It does not appear in your formula for f(x)

    Do you mean
    f(x) = (sqrt16) - x or sqrt(16-x)?

    The first case is trivial: 4 -x.

    For the second case, use the Taylor series formula.

    At x=0, the derivative of f(x) is
    f'(x) =
    (-1/2)/(16-x)^1/2 = -1/8

    In linear approximation,
    f(x) = f(0) + f'(0)*x
    = 4 - (x/8)

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    Suppose that you can calculate the derivative of a function using the formula f(x) = 2f(x) + 4x. If the output value of the function at x=4 is 3 estimate the value of the function at 4.012. Linear Approximation right?
  2. calculus

    Use the linearization approximation (1+x)^k=1+kx to find an approximation for the function f(x)=(1/square root of 4+x) for values of x near zero.
  3. calculus

    Use the linearization approximation (1+x)^k=1+kx to find an approximation for the function f(x)=(1/square root of 4+x) for values of x near zero.
  4. Math

    Find an equation of the line that bisects the obtuse angles formed by the lines with equations 3x-y=1 and x+y=-2. a. (3√2 +√10)x-(√10 + √2)y-2√10+√2=0 b. (3√2 - √10)x+(√10 - √2)y+2√10+√2=0 …
  5. Calculus

    Use linear approximation, i.e. the tangent line, to approximate (the 3 is inside the v part if you know what I mean, it's not 3 times sqrt) 3√125.2 as follows: Let f(x) = 3√x. The equation of the tangent line to f(x) at …
  6. calc b

    lINEAR APPROXIMATION; find a linearization at a suitably chosen interger near X at which the given function and its derivative are easy to evaluate; f(x)=1+X x=8.1
  7. Math (linear approximation)

    Find a linear approximation of the function f(x)=(1+x)^(1/4) at a=1, and use it to approximate the numbers (.95)^(1/4) and (1.1)^(1/4). Round your answers to the nearest thousandth Cheers in advance!
  8. AP CALC. AB

    1. Let f be the function given by f(x)=x^2+4x-8. The tangent line to the graph at x = 2 is used to approximate values of f . For what value(s) of x is the tangent line approximation twice that of f ?
  9. linear approximation

    a) Find the linear approximation of the function f(x)=4cos(3x^2) near x = 0 b) Use the approximation found in part (a) to estimate the value of f(pi/20)
  10. calc

    For each function below find the best linear approximation (linearization) at the given value. f(x) = x^-1 at x = 2 y = 1/2 f ' (x) = -1x^-2 at x = 2 : -1/4 y - 1/2 = -1/4 (x-2) y - 1/2 = -1/4x + 1/2 y = -1/4x + 1 Use the appropriate …

More Similar Questions

Post a New Question