How do I evaluate the limit? lim(x->infinity) sqrt(x+3)-sqrt(x+1) can someone he

Question

How do I evaluate the limit?
lim(x->infinity) sqrt(x+3)-sqrt(x+1)

can someone help me pleaase?

Explanation / Answer

lim(x-->8) v(9x6 - x) / (x³ + 1) Look in the denominator at the x to the highest power. In this case it's x³. Divide everything by x³. Remember that when under the radical x³ will become x6: lim(x-->8) v((9x6/x6) - (x/x6)) / ((x³/x³) + (1/x³)) Simplify: lim(x-->8) v(9 - (1/x5)) / (1 + (1/x³)) Plug in infinity for x: v(9 - (1/8)) / (1 + (1/8)) Remember that a constant divided by infinity goes to zero: v(9 - 0) / (1 + 0) = v(9) = 3

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