Question
If f (x) = 4x2 - 7x - 2/x - 2, x ≠ 2 find a ∂ > 0 such that |f (x) - 9| < 1/100 for 0 < |x - 2| < ∂. Hence show that lim x→2 f (x) = 9.
Answer :
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Skip in 10
To solve this problem numerically, let's first clarify the given function and then proceed step-by-step. The function given is: \[ f(x) = \frac{4x^2 - 7x - 2}{x - 2}, \quad \text{where} \, x \neq 2 \] We are tasked with finding a value of \(\delta > 0\) such that: \[ |f(x) - 9| < \frac{1}{100} \quad \text{for} \quad 0 < |x - 2| < \delta \] This will help us demonstrate that: \[ \lim_{x \to 2} f(x) = 9 \] ### Step 1: Simplify the function \(f(x)\) First, let's simplify the expression for \(f(x)\): \[ f(x) = \frac{4x^2 - 7x
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