Q.Evaluate $\displaystyle\lim_{x\to2}(x^2+3x-1)$.

Since this is a polynomial, which is defined everywhere with no gaps or breaks, its limit at any point can be found by simply substituting that point directly.

Step 1 — Recognise the function type. $f(x)=x^2+3x-1$ is a polynomial, and polynomials are defined for every real number with no jumps or breaks — so direct substitution is valid here (by the algebra of limits, since each piece $x^2$, $3x$, and $-1$ has a limit at $x=2$ equal to its value there, and the sum/difference rule combines them).

Step 2 — Substitute. $\lim_{x\to2}(x^2+3x-1) = 2^2+3(2)-1 = 4+6-1 = 9$. …

Arithmetic slips when substituting (e.g. computing $3(2)$ as $5$ instead of $6$) are the main source of error here — since the method itself …