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sqrt(3+2*x)
Limit of the function/ sqrt(3+2*x)

Limit of the function sqrt(3+2*x)

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The solution

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       _________
 lim \/ 3 + 2*x 
x->0+
lim⁡x→0+2x+3\lim_{x \to 0^+} \sqrt{2 x + 3} 
Limit(sqrt(3 + 2*x), x, 0)
Lopital's rule
There is no sense to apply Lopital's rule to this function since there is no indeterminateness of 0/0 or oo/oo type
The graph
02468-8-6-4-2-101005
Plot the graph
Rapid solution [src] 
  ___
\/ 3
3\sqrt{3}
Expand and simplify
One‐sided limits [src] 
       _________
 lim \/ 3 + 2*x 
x->0+
lim⁡x→0+2x+3\lim_{x \to 0^+} \sqrt{2 x + 3} 
  ___
\/ 3
3\sqrt{3} 
= 1.73205080756888
       _________
 lim \/ 3 + 2*x 
x->0-
lim⁡x→0−2x+3\lim_{x \to 0^-} \sqrt{2 x + 3} 
  ___
\/ 3
3\sqrt{3} 
= 1.73205080756888
= 1.73205080756888
Other limits x→0, -oo, +oo, 1
lim⁡x→0−2x+3=3\lim_{x \to 0^-} \sqrt{2 x + 3} = \sqrt{3}
More at x→0 from the left
lim⁡x→0+2x+3=3\lim_{x \to 0^+} \sqrt{2 x + 3} = \sqrt{3}
lim⁡x→∞2x+3=∞\lim_{x \to \infty} \sqrt{2 x + 3} = \infty
More at x→oo
lim⁡x→1−2x+3=5\lim_{x \to 1^-} \sqrt{2 x + 3} = \sqrt{5}
More at x→1 from the left
lim⁡x→1+2x+3=5\lim_{x \to 1^+} \sqrt{2 x + 3} = \sqrt{5}
More at x→1 from the right
lim⁡x→−∞2x+3=∞i\lim_{x \to -\infty} \sqrt{2 x + 3} = \infty i
More at x→-oo
Numerical answer [src] 
1.73205080756888
1.73205080756888
The graph
Limit of the function sqrt(3+2*x)
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