Evaluate the following limits \(\lim _{x\to 4}\frac{4x+3}{x-2}\) [ MP Board2025]

We are given:

\(\underset{x\to 4}{\lim ⁡}\frac{4x+3}{x−2}\)

Step 1: Substitute \(x=4\) directly into the expression.

Numerator:

\(4x+3=4(4)+3=16+3=19\)

Denominator:

\(x−2=4−2=2\)

Step 2: Simplify the result.

\(\frac{19}{2}\)

Final Answer:

\(\frac{19}{2}\)