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lim_(x rarr4)(x-4)/(x-4)

lim⁡x→4x−4x−4 \lim _{x \rightarrow 4} \frac{x-4}{x-4}

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Full solution

Q. lim⁡x→4x−4x−4 \lim _{x \rightarrow 4} \frac{x-4}{x-4}
  1. Identify Form: Identify the form of the expression when xx is substituted by 44. Substituting x=4x = 4, we get 4−44−4=00\frac{4-4}{4-4} = \frac{0}{0}, which is an indeterminate form.
  2. Simplify Expression: Simplify the expression (x−4)/(x−4)(x-4)/(x-4). Since the numerator and denominator are the same, (x−4)/(x−4)(x-4)/(x-4) simplifies to 11 for all x≠4x \neq 4.
  3. Determine Limit: Determine the limit as xx approaches 44. Since the simplified expression is 11 for all x≠4x \neq 4, the limit as xx approaches 44 of (x−4)/(x−4)(x-4)/(x-4) is 11.

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