Question 4 of 70beginner🔧 ApplyNumerical1 mark

Evaluate the following limits in Exercises 1 to 22. lim⁡x→44x+3x−2\lim_{x \to 4} \frac{4x + 3}{x - 2}

Correct Answer

19/2 or 9.5

Exercise: EXERCISE 12.1 | Q: 4 | (Page Page 21)
For More Understanding

Explanation

This is a straightforward limit evaluation. The context shows that when evaluating a limit at a point, we first check if the function is defined at that point. For example, in the context, we see: 'We have lim(x→1) (x² + 1)/(x + 100) = (1² + 1)/(1 + 100) = 2/101'. Similarly, here the function f(x) = (4x + 3)/(x - 2) is defined at x = 4 since the denominator doesn't become zero. Therefore, we can directly substitute x = 4 into the function.

Solution Steps

  1. Step 1: Check if the function is defined at x = 4. Denominator = 4 - 2 = 2 ≠\neq 0, so the function is defined.

  2. Step 2: Since the function is defined at x = 4, directly substitute x = 4.

  3. Step 3: lim(x→4) (4x + 3)/(x - 2) = (4(4) + 3)/(4 - 2) = (16 + 3)/2 = 19/2 = 9.5

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