Question

Find the limit. use l'hospital's rule if appropriate. if there is a more elementary method, consider using it. lim x→4 x2 − 16 x2 − 4x

Answer 1

To find the limit, factor the numerator and denominator, cancel out the common factor, and substitute the limit value to calculate the final answer.

Step-by-step explanation:

To find the limit of lim x→4 (x² - 16) / (x² - 4x), we can simplify the expression by factoring the numerator and denominator. The numerator can be factored as (x + 4)(x - 4), and the denominator can be factored as x(x - 4). Canceling out the common factor (x - 4), we are left with (x + 4) / x. Now we can substitute the limit value of x=4 into the simplified expression and calculate the limit.

lim x→4 (x + 4) / x = 8 / 4 = 2.

=

Answer 2

Probably you are supposed to compute


`\displaystyle\lim_(x\to4)(x^2-16)/(x^2-4x)`

Factorize the numerator and denominator, then simplify:


`\displaystyle\lim_(x\to4)((x-4)(x+4))/(x(x-4))=\lim_(x\to4)\frac{x+4}x=\frac{4+4}4=2`