ln(x) när x->∞
When x approaches infinity, the natural logarithm of x, denoted as ln(x), also approaches infinity
When x approaches infinity, the natural logarithm of x, denoted as ln(x), also approaches infinity.
The natural logarithm function ln(x) is the inverse function of the exponential function e^x. It measures the power to which e (approximately equal to 2.71828) must be raised to obtain a given value of x.
As x becomes larger and larger, ln(x) also increases without bound. This is because the exponential growth of e^x far exceeds any linear growth, which causes the logarithm to increase indefinitely.
To visually understand this, consider the graph of the natural logarithm function. As x approaches infinity on the x-axis, the corresponding value of ln(x) on the y-axis goes towards positive infinity, but at a decreasing rate. In other words, ln(x) grows larger and larger, but the rate of growth slows down as x becomes increasingly large.
Therefore, the limit of ln(x) as x approaches infinity is +∞. Written mathematically, it can be expressed as:
lim(x→∞) ln(x) = +∞
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