discuss singularity x=infinity
Answers
Step-by-step explanation:
In mathematics, a singularity is in general a point at which a given mathematical object is not defined, or a point where the mathematical object ceases to be well-behaved in some particular way, such as by lacking differentiability or analyticity.[1][2][3][4]
For example, the real function
{\displaystyle f(x)={\frac {1}{x}}}f(x)={\frac {1}{x}}
has a singularity at {\displaystyle x=0}x=0, where it seems to "explode" to {\displaystyle \pm \infty }\pm \infty and is hence not defined. The absolute value function {\displaystyle g(x)=|x|}{\displaystyle g(x)=|x|} also has a singularity at x = 0, since it is not differentiable there.[1][5]
The algebraic curve defined by {\displaystyle \{(x,y):y^{3}-x^{2}=0\}}{\displaystyle \{(x,y):y^{3}-x^{2}=0\}} in the {\displaystyle (x,y)}(x,y) coordinate system has a singularity (called a cusp) at {\displaystyle (0,0)}(0,0). For singularities in algebraic geometry, see singular point of an algebraic variety. For singularities in differential geometry, see singularity theory.