Solve algebraically: NKS \lim_{x \to 3} \frac{3-x}{5-\sqrt{x^2+16}}

hestyllvql

hestyllvql

Answered question

2022-04-21

Solve algebraically:

limx33x5x2+16

Answer & Explanation

Makayla Santiago

Makayla Santiago

Beginner2022-04-22Added 19 answers

Try multiplying the numerator and denominator by the conjugate of the denominator:
Multiply by
5+x2+165+x2+16
limx33-x5-x2+16·5+x2+165+x2+16=limx3(3-x)(5+x2+16)25-(x2+16)
Then note that you have a difference of squares in the denominator:
25(x2+16)=9x2=(3x)(3+x)
Now, you can cancel the factor 3x, as it appears in both the numerator and denominator.

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