Calculus

The table below gives selected values of a twice differentiable function f(x)

x|. -7. -6. -4. -2.

f(x)|. 0. -1. -2. 0

f'(x)|. 3. 2. -1. 7

What is the limit of f(3x-1)/(x^2)-4 as x approaches -2?

What is the limit of f(f(x))/5x + 20 as x approaches -4?

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  1. f(3(-2)-1)/(-2)^2 - 4 = f(-7)/4 - 4 = 0 - 4 = -4
    Now, if you meant
    f(3x-1)/(x^2-4) then that would be 0/0 which is a problem.
    But, l'Hôpital's Rule says that the limit is the same as
    d/dx f(3x-1) / d/dx (x^2-4)
    = (f'(3x-1) * 3) / (2x)
    = (3*3) / -6
    = -3/2

    see what you can do with the other one

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    oobleck

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