# What is carrying capacity ?

The carrying capacity of a species is the maximum population of that species that the environment can sustain indefinitely, given available resources. It acts as an upper limit on population growth functions.

In the normal course of events, barring extreme circumstances, the population will not surpass the carrying capacity. However, some extreme circumstances (such as the sudden influx of more members of the population from external areas, along with certain natural cyclic variations) can cause the population to temporarily exceed the carrying capacity. This leads to a sharp decrease in the population (a "population crash") as resources become more scarce, leading to starvation and dehydration, as well as deaths caused by fighting over the now-scarce resources.

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Carrying capacity refers to the maximum population size of a species that an environment can sustain indefinitely, given the resources available in that environment. It is determined by factors such as food, water, shelter, and other resources necessary for the survival and reproduction of the species. When a population exceeds the carrying capacity of its environment, resources become scarce, leading to increased competition, reduced reproductive success, and potentially population decline through factors like starvation, disease, or emigration. Understanding carrying capacity is essential in ecology and conservation biology for predicting and managing populations and ecosystems.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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- If the average value of the function f on the interval [1, 5] is 3, and the average value on the interval [5, 7] is 2, how do you find the average value on the interval [1, 7]?
- What is the arc length of #f(x)=2/x^4-1/(x^3+7)^6# on #x in [3,oo]#?
- A particle is constrained to move in #Q_1#, in a parabolic groove # y = x^2#. It was at O, at t = 0 s. At time t s, its speeds in the directions Ox and Oy are 5 and 12 cm/s, respectively. How do you prove its direction makes #67^o22'49''# with Ox?
- What is the general solution of the differential equation # (d^2y)/(dx^2) + 3dy/dx + 2y = 2sinx#?

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