1. ## limits question

How can we know if the limits to these actually exist and if they do, what are they.

1) lim (x---->0) {(sqrt(1+2x)) - (sqrt(1-3x))}/{x}

2) lim (x---->1) {3(x^4) - 8(x^3) + 5}/{(x^3) - (x^2) -x -1}

3) lim (x----->infinity) {(sqrt((x^2) +1) - (sqrt((x^2) -1)}

2. Can we see your attempt please? Because there is no use of just giving up the answers...

3. 1. Try rationalising the numerator.

2. Divide numerator and denominator by the highest power of x.

4. Originally Posted by maximus101
How can we know if the limits to these actually exist and if they do, what are they.

1) lim (x---->0) {(sqrt(1+2x)) - (sqrt(1-3x))}/{x}
Multiply both numerator and denominator by [tex]\sqrt{1+ 2x}+ \sqrt{1- 3x}

2) lim (x---->1) {3(x^4) - 8(x^3) + 5}/{(x^3) - (x^2) -x -1}
What is the value at x= 1?

3) lim (x----->infinity) {(sqrt((x^2) +1) - (sqrt((x^2) -1)}
multiply numerator and denominator by $\sqrt{x^2+ 1}+ \sqrt{x^2- 1}$

These are essentiall "Pre-Calculus" problems. Strange that you would post them with Analysis problems.