Question 3 of 70beginner🔧 ApplyNumerical1 mark

Evaluate the following limits in Exercises 1 to 22. lim⁡r→1πr2\lim_{r \to 1} \pi r^2

Correct Answer

π

Exercise: EXERCISE 12.1 | Q: 3 | (Page Page 21)
For More Understanding

Explanation

This is a straightforward limit evaluation. The function f(r) = πr² is a polynomial function (constant π multiplied by r²), which is continuous everywhere. From the context, we see examples like lim(x→1)(x² + 1)/(x + 100) = (1² + 1)/(1 + 100) = 2/101, demonstrating that for continuous functions, we can directly substitute the limiting value. Similarly, the context shows lim(x→1) x² = 1, confirming that polynomial limits are evaluated by substitution.

Solution Steps

  1. Step 1: Identify that f(r) = πr² is a continuous function (polynomial form).

  2. Step 2: Apply direct substitution: lim(r→1) πr² = π(1)²

  3. Step 3: Simplify: π(1)² = π(1) = π

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