The limit of the function f(x)=[tex]x^{3}-1[/tex]/x-1 as x approaches 1 is 3.
What is limit?
Limit is the value that a function approaches as the value of variable approaches some value. They are essential to calculas and mathematical analysis and are use to define continuity , derivatives and integrals. It can change value of function at different values of x.
How to find limit?
We have been given a function f(x)=[tex]x^{3}-1[/tex]/x-1 and we have to find the limit of function.
F(x)=[tex]x^{3} -1[/tex] /(x-1) [[tex]x^{3} -y^{3} =x^{2} +y^{2} +xy[/tex]]
[tex]\lim_{x \to \0}x^{3}-1/x-1[/tex]
[tex]\lim_{x \to \0} (x-1)(x^{2} +1+x)[/tex]/x-1
[tex]\lim_{x \to \0} x^{2} +x+1[/tex]
change limit by putting x=1-h
[tex]\lim_{h \to \0} (1-h)^{2} +1+1-h[/tex]
Put the value of h=0.
=1+1+1
=3
Hence the limit of the function [tex]x^{3}-1/x-1[/tex] is 3.
Learn more about limits at https://brainly.com/question/27517662
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