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Calculus

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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.

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