Final answer to the problem
Step-by-step Solution
Specify the solving method
Expand the expression $\left(21+x\right)^2$ using the square of a binomial: $(a+b)^2=a^2+2ab+b^2$
Learn how to solve limits by direct substitution problems step by step online.
$\lim_{x\to0}\left(\frac{441+42x+x^{2}-441}{x}\right)$
Learn how to solve limits by direct substitution problems step by step online. Find the limit of ((21+x)^2-441)/x as x approaches 0. Expand the expression \left(21+x\right)^2 using the square of a binomial: (a+b)^2=a^2+2ab+b^2. Subtract the values 441 and -441. If we directly evaluate the limit \lim_{x\to 0}\left(\frac{42x+x^{2}}{x}\right) as x tends to 0, we can see that it gives us an indeterminate form. We can solve this limit by applying L'H么pital's rule, which consists of calculating the derivative of both the numerator and the denominator separately.