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let f(x)=0f(x)=0 and g(x)=xxg(x)=\frac{x}{x} explain, why lim⁡x→2(f(x))=0\lim_{x\to 2}(f(x))=0, lim⁡x→0(g(x))=0\lim_{x\to 0}(g(x))=0 and why lim⁡x→2(g(f(x))\lim_{x\to 2}(g(f(x)) does not exist

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Q. let f(x)=0f(x)=0 and g(x)=xxg(x)=\frac{x}{x} explain, why lim⁡x→2(f(x))=0\lim_{x\to 2}(f(x))=0, lim⁡x→0(g(x))=0\lim_{x\to 0}(g(x))=0 and why lim⁡x→2(g(f(x))\lim_{x\to 2}(g(f(x)) does not exist
  1. extit{f}(x) Approach 22: extit{f}(x) is defined as 00 for all xx, so as xx approaches 22, extit{f}(x) remains 00.
  2. Constant Function Limit: Since f(x)f(x) is a constant function, the limit as xx approaches any number is just the constant value itself.
  3. extit{f}(x) Limit Calculation: Therefore, extlimxo2(extitf(x))=0 ext{lim}_{x o 2}( extit{f}(x)) = 0.
  4. ext{g(x) Definition:} ext{g(x)} is defined as rac{x}{x}, which simplifies to 11 for all xx except x=0x = 0, where it is undefined.
  5. extit{g}(x) Limit Error: As xx approaches 00 from either side, the value of extit{g}(xx) approaches 11, not 00. This is a mistake.

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