Calculus

posted by .

The linearization at a=0 to sqrt(1+6x) is A+Bx where A is: ____ and where B is : ______

  • Calculus -

    Let f(x)=sqrt(1+6x)
    then f'(x)=3/sqrt(6*x+1)
    and f'(0)=3
    Thus the slope of the curve is 3 at x=0.
    f(0)=1 means that the tangent to the curve passes through (0,1)=(x0,y0).
    So the linearization is
    y=Ax+B
    =Slope(x-x0)+y0
    =3(x-0)+1
    =3x+1
    Identify A and B for your answer.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    Please look at my work below: Solve the initial-value problem. y'' + 4y' + 6y = 0 , y(0) = 2 , y'(0) = 4 r^2+4r+6=0, r=(16 +/- Sqrt(4^2-4(1)(6)))/2(1) r=(16 +/- Sqrt(-8)) r=8 +/- Sqrt(2)*i, alpha=8, Beta=Sqrt(2) y(0)=2, e^(8*0)*(c1*cos(0)+c2*sin(0))=c2=2 …
  2. Calculus

    Find the linearization of f(x)= sqrtx at x=25 and use the linearization to approximate sqrt25.2 This is my math: 5+ 1/10 * (25.2-25) but it's wrong.
  3. Grammar

    Fill in the sentences with adverbs. Do not repeat. 1.______ my friend and I _____ went _____. 2.We had _______ wanted to go ____, so we went _____ ______ and ____. 3. When we arrived _____, it was ____ dark, so we ____ went _____. …
  4. MATH

    PLEASE EXPLAIN HOW TO FIND THE COMMON RATIO FOR THE GEOMETRIC SEQUENCE 16, 40. 100,____, ____ AND 81,54, ______,______,______
  5. CALCULUS

    Consider the function f(x)=sqrt(2–5x^2), –5≤x≤1. The absolute minimum value is ____ and this occurs at x equals ______?
  6. Calculus

    Find the local linearization of f(x) near x=0 and use it to approximate the value of a. f(x)=sqrt((b^2)+x) a=sqrt(26)
  7. Intergration: Measurement (Math)

    I don't get it. I need to find out these conversions. 15,000 g= ____ kg 5,000 mL= ____ L 75 mL= ____ L 390 mL= ____ L 0.03 m= ____ mm 6 m= _____ mm 2.48 L= ______ mL 43.2 L= ______ mL 807 mL= _____ L 3,751 m= _____ km
  8. Calculus

    Find the local linearization of g(x)=sqrt 4x near x=2 use local linearization to estimate g(2.05) is your estimate too high or too low?
  9. Math Calculus

    f(x) = (x^3+5x^2-28x-32)/(x^3-18x^2+105x-196) which can be written as f(x) = [(x+1)(x-4)(x+8)]/[(x-7)^2(x-4) The domain of the function f(x), in interval notation from left to right, is ____ U ____ U ______. The root(s) of f(x), in …
  10. Calculus Please help!

    The linearization at a=0 to sqrt(1+2x) is A+Bx where A is____ and where B is _____?

More Similar Questions