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A Solution to Discontinuous Problems in Higher Mathematics
To judge the discontinuity of function f(x), we need to ask its limit first. According to the formula given in the title, we can get:

f(x) = lim(n→∞)? √( 1+|x|^(3n))

For | x |

f(x) = lim(n→∞)? √( 1+|x|^(3n)) = 1

For |x| > 1, because the value of | x | (3n) is close to positive infinity, therefore:

f(x) = lim(n→∞)? √ (1+| x | (3n)) = +∞

When x = 1 or x =-1, |x| = 1, the value of f(x) is:

f( 1) = lim(n→∞)? √( 1+ 1^(3n)) = 2

f(- 1) = lim(n→∞)? √( 1+(- 1)^(3n)) = 0

Therefore, the limit of f(x) at x = 1 exists and is equal to 2, at x =-1 exists and is equal to 0, and at | x | 1 the limits are 1 and +∞ respectively.

Next, we can draw an image of f(x) to see if there are any discontinuities. First, we can mark x =-1 and x = 1 on the number axis, and then draw the image of f(x) on the corresponding interval according to the above limit results. We can find that the value of f(x) jumps at x =-1, so x =-1 is a discontinuous point of f(x).

To sum up, f(x) has discontinuous points at x =-1, and other points are continuous.