Find $\displaystyle\lim_{x\to 1}\frac{2x^3+3x^2-1}{5x-2}$.

This is a straightforward limit evaluation by direct substitution—the key insight is recognizing when you can simply plug in the value. Since the denominator doesn't equal zero at $x=1$, both numerator and denominator are continuous there, so the limit of a quotient equals the quotient of the limits. Just evaluate the top and bottom at $x=1$ and simplify.

This is a straightforward limit evaluation by direct substitution—the key insight is recognizing when you can simply plug in the value. Since the denominator doesn't equal zero at $x=1$, both numerator and denominator are continuous there, so the limit of a quotient equals the quotient of the limits. Just evaluate the top and bottom at $x=1$ and simplify.