Find the limit. lim x → 2 x 2 + 5 \lim_{x\rarr2}\sqrt{x^2+5} lim x → 2 x 2 + 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z">

Here, we wanna find the limit of the function, the square root of x squared plus 5 as x approaches 2. So with this basic root, we can go ahead and find the limit by just plugging in this x value. So this ends up giving me the square root of 2 squared plus 5. Now 2 squared is 4 plus 5 will give me 9, so this is the square root of 9, which we know is just equal to 3. So the limit of this function as x approaches 2 is 3. Thanks for watching. I'll see you in the next one.

22. Limits & Continuity

Finding Limits Algebraically

Precalculus

NEW 22. Limits & Continuity

Finding Limits Algebraically

Struggling with Precalculus?

Join thousands of students who trust us to help them ace their exams!Watch the first video

Multiple Choice

Find the limit.
$\lim_{x\rarr2}\sqrt{x^2+5}$

$0$

$2$

$3$

$5$

Verified step by step guidance

Identify the function for which you need to find the limit: $ \lim_{x \to 2} \sqrt{x^2 + 5} $.

Understand that the limit asks what value $ \sqrt{x^2 + 5} $ approaches as $ x $ gets closer to 2.

Substitute $ x = 2 $ directly into the function $ \sqrt{x^2 + 5} $ to check if the function is continuous at $ x = 2 $.

Calculate $ \sqrt{2^2 + 5} $ to see if the function is defined and continuous at $ x = 2 $.

Conclude that since the function is continuous at $ x = 2 $, the limit is simply the value of the function at $ x = 2 $.

5:21m

Watch next

Master Finding Limits by Direct Substitution with a bite sized video explanation from Patrick

Start learning

Finding Limits Algebraically practice set

Problem sets built by lead tutors

Expert video explanations

Go to Practice

Struggling with Precalculus?

Find the limit.limx→2x2+5\lim_{x\rarr2}\sqrt{x^2+5}limx→2x2+5

Watch next

Finding Limits Algebraically practice set

Find the limit.
$\lim_{x\rarr2}\sqrt{x^2+5}$