The major cause of blurring and unsharp images of objects observed through very large telescopes at the extreme limit of magnification is poor optical polish achievable on large mirrors.

Option 1, air turbulence of the Earth`s atmosphere, refers to the phenomenon of the Earth`s atmosphere causing distortion in the image due to the varying density and temperature of the air. While this can indeed cause some blurring, it is not the major cause mentioned in the question.

Option 3, poor tracking capacities of telescopes, refers to the ability of the telescope to remain pointed at a specific object as the Earth rotates. While this can affect image stability, it is not specifically related to blurring or unsharpness.

Option 4, varying density of air in the Earth`s atmosphere, is similar to option 1 and also refers to air turbulence causing distortion in the image. Again, while this can contribute to blurring, it is not the major cause mentioned in the question.

Option 2, poor optical polish achievable on large mirrors, is the correct answer provided. Large telescope mirrors can be challenging to polish to the necessary precision, leading to imperfections that cause blurring and unsharpness in the observed images.

Therefore, the correct answer is option 2.