Question

Evaluate: Lim x ²cos3x ÷ x³ + 4x²

x tend to 0

Answer 1

$\text{lim}\frac{x^2cos3x}{x^3}+4x^2 \text{ as x tends to 0}$

$=\text{lim}\frac{cos3x}{x}+4x^2$

$=\text{lim}\frac{cos3x}{x}+lim4x^2$

$\text{Using l'hopital rule we find limit for } \text{lim}\frac{cos3x}{x}$

$=lim(-3sinx)\text{ as x tends to 0 }$

$=0$

$lim4x^2=0$ as x tends to 0

$Hence \text{ lim}\frac{x^2cos3x}{x^3}+4x^2 =0$