We now have lim x → [infinity] (4x − ln(x)) = lim x → [infinity] 4x 1 − ln(x) 4x . let's first focus on lim x → [infinity] ln(x) 4x . since ln(x) → [infinity] as x → [infinity], then this limit is indeterminate of type [infinity]/[infinity]. using l'hospital's rule, we find: lim x → [infinity] ln(x) 4x = lim x → [infinity] 1 = 0 .

Identify the function that contains the data in the following table: x     -2         0         2         3         5     f(x)     5         3         1         2         4     possible answers: f(x) = |x| + 1 f(x) = |x - 2| f(x) = |x - 2| - 1 f(x) = |x - 2| + 1

2. (09.01 lc) a function is shown in the table. x g(x) −3 17 −1 −3 0 −4 2 13 which of the following is a true statement for this function? (5 points) the function is increasing from x = −3 to x = −1. the function is increasing from x = −1 to x = 0. the function is decreasing from x = 0 to x = 2. the function is decreasing from x = −3 to x = −1.

Javier bought a painting for $150. each year, the painting's value increases by a factor of 1.15. which expression gives the painting's value after 77 years?