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(3x1)/(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 answer

f(3(2)1)/(2)^2  4 = f(7)/4  4 = 0  4 = 4
Now, if you meant
f(3x1)/(x^24) 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(3x1) / d/dx (x^24)
= (f'(3x1) * 3) / (2x)
= (3*3) / 6
= 3/2
see what you can do with the other one
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