Question 25 of 70beginner🔧 ApplyShort Answer1 mark

Find lim⁡x→5f(x)\lim_{x \to 5} f(x), where f(x)=∣x∣−5f(x) = |x| - 5

Correct Answer

0

Exercise: EXERCISE 12.1 | Q: 27 | (Page Page 22)
For More Understanding

Explanation

The question asks for the limit of f(x) = |x| - 5 as x approaches 5. Following the methodology shown in the context, we need to check both left-hand and right-hand limits. Near x = 5, x is positive, so |x| = x. Thus f(x) = x - 5 near x = 5. Both limits approach 5 - 5 = 0, so the limit is 0.

Solution Steps

  1. Step 1: Near x = 5, x is positive, so |x| = x

  2. Step 2: Thus f(x) = x - 5 near x = 5

  3. Step 3: lim(x→5⁻) f(x) = lim(x→5⁺) f(x) = 5 - 5 = 0

  4. Step 4: Since both limits are equal, lim(x→5) f(x) = 0

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