Question 1 of 70beginner🔧 ApplyNumerical1 mark

Evaluate the following limits in Exercises 1 to 22.

lim⁡x→3x+3\lim_{x \to 3} x + 3

Correct Answer

6

Exercise: EXERCISE 12.1 | Q: 1 | (Page Page 21)
For More Understanding

Explanation

This is a straightforward limit evaluation. The function f(x) = x + 3 is a polynomial function, which is continuous for all real numbers. For continuous functions, the limit can be evaluated by direct substitution. The context shows similar examples where limits are evaluated by substituting the value directly, such as in Example 2(i) where lim(x→1) of (x² + 1)/(x + 100) is found by direct substitution.

Solution Steps

  1. Step 1: Identify the function type. The function f(x) = x + 3 is a polynomial function, which is continuous for all real values of x.

  2. Step 2: Apply direct substitution. Since polynomial functions are continuous everywhere, we can evaluate the limit by directly substituting x = 3.

  3. Step 3: Calculate the value. lim(x→3)(x + 3) = 3 + 3 = 6

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