Question

I am trying to find the limit for the attached problem. Could someone please explain the process of how to find this limit?

Answer 1

hint: multiply top and bottom by 1/x

Answer 2

Why?

Answer 3

multiply 1/x in the denominator to get

2x - 7

(1/x)*(2x-7)

(1/x)*2x - (1/x)*7

2x/x - 7/x

2 - (7/x)

Answer 4

or you can think of it as dividing each term in the denominator by x

Answer 5

why do this? because you'll be taking advantage of the fact that the limit as x--> infinity for 7/x is 0, so that piece goes away

Answer 6

you have to apply this in the numerator as well

so

sqrt(5x^2 + 2x)*(1/x)

(1/x)*sqrt(5x^2 + 2x)

sqrt( (1/x^2) )*sqrt(5x^2 + 2x)

sqrt( (1/x^2)* (5x^2 + 2x) )

sqrt( (1/x^2)* (5x^2) + (1/x^2)* (2x) )

sqrt( 5x^2/x^2 + 2x/x^2 )

sqrt( 5 + 2/x )

Answer 7

this means

sqrt(5x^2 + 2x)/( 2x - 7 )

turns into

sqrt( 5 + 2/x )/( 2 - 7/x)

I'll let you finish up