Mister Exam

Other calculators:

Limit of the function/ log(x^2+2*x)

Limit of the function log(x^2+2*x)

at →
v

For end points:

The graph:

from to

Piecewise:

The solution

You have entered [src] 
        / 2      \
 lim log\x  + 2*x/
x->0+
lim⁡x→0+log⁡(x2+2x)\lim_{x \to 0^+} \log{\left(x^{2} + 2 x \right)} 
Limit(log(x^2 + 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
02468-8-6-4-2-1010-1010
Plot the graph
Rapid solution [src] 
-oo
−∞-\infty
Expand and simplify
One‐sided limits [src] 
        / 2      \
 lim log\x  + 2*x/
x->0+
lim⁡x→0+log⁡(x2+2x)\lim_{x \to 0^+} \log{\left(x^{2} + 2 x \right)} 
-oo
−∞-\infty 
= -8.19804051398379
        / 2      \
 lim log\x  + 2*x/
x->0-
lim⁡x→0−log⁡(x2+2x)\lim_{x \to 0^-} \log{\left(x^{2} + 2 x \right)} 
-oo
−∞-\infty 
= (-8.18273783923912 + 3.14159265358979j)
= (-8.18273783923912 + 3.14159265358979j)
Other limits x→0, -oo, +oo, 1
lim⁡x→0−log⁡(x2+2x)=−∞\lim_{x \to 0^-} \log{\left(x^{2} + 2 x \right)} = -\infty
More at x→0 from the left
lim⁡x→0+log⁡(x2+2x)=−∞\lim_{x \to 0^+} \log{\left(x^{2} + 2 x \right)} = -\infty
lim⁡x→∞log⁡(x2+2x)=∞\lim_{x \to \infty} \log{\left(x^{2} + 2 x \right)} = \infty
More at x→oo
lim⁡x→1−log⁡(x2+2x)=log⁡(3)\lim_{x \to 1^-} \log{\left(x^{2} + 2 x \right)} = \log{\left(3 \right)}
More at x→1 from the left
lim⁡x→1+log⁡(x2+2x)=log⁡(3)\lim_{x \to 1^+} \log{\left(x^{2} + 2 x \right)} = \log{\left(3 \right)}
More at x→1 from the right
lim⁡x→−∞log⁡(x2+2x)=∞\lim_{x \to -\infty} \log{\left(x^{2} + 2 x \right)} = \infty
More at x→-oo
Numerical answer [src] 
-8.19804051398379
-8.19804051398379
    © Mister Exam – Calculator