How does a fish's swim bladder affect its overall density?

Answer 1
The non-natural vertebrate group, commonly known as #fishes#, are mainly consisted by aquatic animals with branchial respiration and have all life cicles directly related to salt or freshwater environments (remember, all aquatic and terrestrial vertebrates are naturally and evolutionary modified forms derived from fishes too, from Sarcopterygian common ancestor).
So, as "fishes" lives inside water, they must control its body flotation (or relative density) by adding or expelling gas from swim bladder. But, how can they do that inside the water, #"IF"# the gas bladder has #"NO" # connections to the mouth in most species of fishes? (except from physostomous Actinopterygians and Australian, South American and African diversity of the only three living species of Dipnoii).

First off, gas or swim bladders are associated with fishes referred to as "Osteichthyes." Actinopterygian (which includes the major group of diversity on freshwater, the Ostariophysii, formed by Siluriformes, Characiformes, Gymnotiformes, and Cypriniformes) and Sarcopterygians (Coelacanthe and related extinct forms of limbed fishes) make up the majority of Osteichthyans, or bony fishes. One characteristic of bony fishes is the swim bladder, a chamber that encapsulates and stores gas inside of it, regulating thus body densities as they want to explore different depths through water column.

How the gas are stored and expelled from the swim bladder? There's an important physiological process that drives the "transformation" of solved blood gases (#O_2 and N_2#) into expanded gases itself, inside the swim bladder. This process takes place on a special tissue called #"gas gland"#, adjacent to the swim bladder, perfused by a numerous tiny vessels (both arterial and venous). When this gland is acidified by physiological commands controlled by the central nervous system of the fish, this acidification leads to the dissociation of blood dissolved oxigen bonded to Hemoglobin, resulting in liberation of oxigen and nitrogen forms of expanded gases inside the swim bladder. The reverse process follows the opposite way, draining gases from the swim bladder into blood stream by turning the pH less acid.
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Answer 2

A fish's swim bladder adjusts its overall density by controlling the volume of gas it contains. When the bladder expands, the fish becomes more buoyant, reducing overall density and allowing it to float. Conversely, deflating the bladder increases density, enabling the fish to descend in the water.

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Answer from HIX Tutor

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.

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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