Question

Evaluate the limit shown above

a.
9/2
b.
3
c.
7/2
d.
limit does not exist


Please select the best answer from the choices provided

a) A
b) B
c) C
d) D

Answer 1

option A 9/2

Explanation:

limit n-> infinity (9n^3+5n-2)/ 2n^3

to plug in limit value we need to simplify the expression

we divide each term by highest exponent in the denominator

we have n^3 in the denominator

so we divide each term by 2n^3

`(9n^3)/(2n^3) + (5n)/(2n^3)  -(2)/(2n^3)`

Simplify it

`(9)/(2) + (5)/(2n^2)  -(2)/(2n^3)`

now we plug in infinity for n

`(9)/(2) + (5)/(2∞^2)  -(2)/(2∞^3)`

1/ infinity is 0

`(9)/(2) +0 -0`

Answer is 9/2