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.

1. Limits and Continuity

Finding Limits Algebraically

Business Calculus

1. Limits and Continuity

Finding Limits Algebraically

Struggling with Business Calculus?

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Multiple Choice

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

$0$

$2$

$3$

$5$

Verified step by step guidance

Rewrite the given limit problem: $ \lim_{x \to 2} \sqrt{x^2 + 5} $. This means we are finding the value that $ \sqrt{x^2 + 5} $ approaches as $ x $ gets closer to 2.

Substitute $ x = 2 $ directly into the expression $ \sqrt{x^2 + 5} $, since the square root function is continuous and defined for all real numbers. Continuity allows us to evaluate the limit by direct substitution.

Perform the substitution: Replace $ x $ with 2 in the expression $ \sqrt{x^2 + 5} $, resulting in $ \sqrt{2^2 + 5} $.

Simplify the expression inside the square root: $ 2^2 = 4 $, so the expression becomes $ \sqrt{4 + 5} $.

Simplify further: $ 4 + 5 = 9 $, so the expression becomes $ \sqrt{9} $. The square root of 9 is 3, which is the value of the limit.

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Struggling with Business Calculus?

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

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Finding Limits Algebraically practice set

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