Question

$\underset{x\to 0}{lim}\frac{(1+x{)}^5-1}{3x+5x^2}$ is equal to

• A. $\frac{3}{5}$
• B. $\frac{5}{3}$
• C. $0$
• D. $1$

Answer 1

The correct option is B $\frac{5}{3}$

Here, we can see that both numerator and denominator are approaching to zero. So it's a 0/0 form.
Hence we can apply L'Hospital's rule to find the limit.
Differentiating both Numerator and denominator - $\underset{x\to 0}{lim}\frac{5(1+x{)}^4}{3+10x}$
We can see that 0/0 form is removed so we can directly put limit value in the expression.
Therefore the answer will be = $\frac{5}{3}$