Thread: [SOLVED] Some help with limits

I have to evaluate the following limits:

a) lim x -> 7
(square root(x+2)) -3 / (x-7

I was unable to solve this

b) lim x -> 0
1/x - 1/(x^2 + x)

Somehow simplified it to 0 / x+1... this makes no sense.

c) lim x -> -infinity
(square root(4x^2 + 1)) / (3x-5)

I somehow got denominator 0 and was unable to solve.

What I did was take the x^2 out of the square root on top and got:

x^2 square root(4+1/x^2) / 3/x - 5/x^2

I am pretty sure the denominators go to zero and and this point I'm lost.


Please help. I can do this and have done similar problems before, just need a little kick start.

Originally Posted by thekrown

I have to evaluate the following limits:

a) lim x -> 7
(square root(x+2)) -3 / (x-7

I was unable to solve this

rationalize the numerator ... multiply by

b) lim x -> 0
1/x - 1/(x^2 + x)

Somehow simplified it to 0 / x+1... this makes no sense.

simplifies to

c) lim x -> -infinity
(square root(4x^2 + 1)) / (3x-5)

first, note that the limit will be less than 0. divide the numerator and denominator by x ...

...

a) Okay gotcha, I can do this.

b) I will redo this, I must of made a repetitive mistake. I will check my work again.

c) I thought in this type of limit we would have to divided by the greatest power of the numerator, in this case x^2. How come just x?

Originally Posted by thekrown

a) Okay gotcha, I can do this.

b) I will redo this, I must of made a repetitive mistake. I will check my work again.

c) I thought in this type of limit we would have to divided by the greatest power of the numerator, in this case x^2. How come just x?

if x goes under the radical, what does it become?

Let me see if I understand this here... see my teacher uses a robotic-teaching method where he says "just do this" and it works. So i haven't learned the proper reasoning to this type of limit.

If what I think you're saying is, the numerator will divide by the greatest power so our square root(4x^2+1) is divided by x^2 to get square root(4+1/x).

Then for the denominator, we use the square root of x^2 and divide the numerator by that?

Is that why it's just x?

Originally Posted by thekrown

Let me see if I understand this here... see my teacher uses a robotic-teaching method where he says "just do this" and it works. So i haven't learned the proper reasoning to this type of limit.

If what I think you're saying is, the numerator will divide by the greatest power so our square root(4x^2+1) is divided by x^2 to get square root(4+1/x).

Then for the denominator, we use the square root of x^2 and divide the numerator by that?

Is that why it's just x?

the full monty ...



now understand that you're really dividing by since

no effect on the numerator, since it is positive for all x.

for the denominator, however ...

since