# Pre-cal

Please determine the following limit if they exist. If the limit doe not exist put DNE.

lim 2x^3 / x^2 + 10x - 12

x->infinity.

Thanks.

1. 👍
2. 👎
3. 👁
1. Intuitively I can see that the numerator gets larger at a faster rate than the denominator.
e.g. if x = 1000, the top is 2 billion, but the bottom is only approx. 1 million, so the expression has a value of about 2000

So the limit approaches infinity.

Algebraically, divide each term by x^2 to get

limit (2x/(1 + 10/x - 12/x^2)

so as x --- infinity
both 10/x and 12/x^2 ---> 0
so we have 2(huge)/1 which appr. infinity

1. 👍
2. 👎

## Similar Questions

1. ### calculus

Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) An = cos(n/8)

2. ### calculus

Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) {0, 4, 0, 0, 4, 0, 0, 0, 4, ...}

3. ### Calculus

Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) limit n approaches infinity of an = e^(−6/sqrt(n))

4. ### calculus

1)A function g is defined for all real numbers and has the following property: g(a+b) - g(a) = 4ab+2b2 find g'(x) A)4 B)-4 C)2x^2 D)4x E)does not exist not so sure where to start 2)If d/dx[f(x)] = g(x) and d/dx[g(x)] = f(3x, then

1. ### Calculus, math

Consider the function below. (If an answer does not exist, enter DNE.) f(x) = e^arctan(7x) I did the problem but I have mistakes on some items. I think the ff. are right: Vertical Asymptote: x = DNE Horizontal Asymptote: y =

2. ### Calculus

Find the limit of the sequence of partial sums whose general term is a sub n equals 100 to the nth power over n factorial . (4 points) A) 10 B) 1 C) Does not exist D) 0

3. ### calculus

Find the absolute extrema of the function (if any exist) on each interval. (If an answer does not exist, enter DNE.) f(x) = square root of (25 − x^2) (a) [−5, 5] minimum (x, y) = (smaller x-value) (x, y) = (larger x-value)

4. ### Math - PreCalc (12th Grade)

Which combination of limit properties is required to evaluate this limit? lim x->((24/x)-2x+2)^3 A) sum, difference, product, root B) sum, difference, product, power C) sum, difference, quotient, power D) sum, difference,

1. ### Calculus

Find the limit of the sequence of partial sums whose general term is an=10^n/n! a) 10 b) 0 ----> my answer. Can you check for me, please? c) 1 d) Does not exist Note: I am between b and d answers

2. ### calculus

Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) An=[(-1)^n]/[8[(n)^(1/2)]]

3. ### Calculus, please check my answers!

1. Evaluate: lim x->infinity(x^4-7x+9)/(4+5x+x^3) 0 1/4 1 4 ***The limit does not exist. 2. Evaluate: lim x->infinity (2^x+x^3)/(x^2+3^x) 0 1 3/2 ***2/3 The limit does not exist. 3. lim x->0 (x^3-7x+9)/(4^x+x^3) 0 1/4 1 ***9 The

4. ### Calculus

Find the limit of the sequence whose general term is a sub n = 1 - 3n/ 4 + n. (5 points) I got Does not Exist. But I think it is wrong. Am I doing this right? A) 1/4 B) 3 C) −3 D) Does not exist