Mister Exam

Other calculators:

log(x+sqrt(1+x^2))
Limit of the function/ log(x+sqrt(1+x^2))

Limit of the function log(x+sqrt(1+x^2))

at →
v

For end points:

The graph:

from to

Piecewise:

The solution

You have entered [src] 
         /       ________\
         |      /      2 |
 lim  log\x + \/  1 + x  /
x->-oo
$$\lim_{x \to -\infty} \log{\left(x + \sqrt{x^{2} + 1} \right)}$$ 
Limit(log(x + sqrt(1 + x^2)), x, -oo)
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
Plot the graph
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to -\infty} \log{\left(x + \sqrt{x^{2} + 1} \right)} = -\infty$$
$$\lim_{x \to \infty} \log{\left(x + \sqrt{x^{2} + 1} \right)} = \infty$$
More at x→oo
$$\lim_{x \to 0^-} \log{\left(x + \sqrt{x^{2} + 1} \right)} = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+} \log{\left(x + \sqrt{x^{2} + 1} \right)} = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-} \log{\left(x + \sqrt{x^{2} + 1} \right)} = \log{\left(1 + \sqrt{2} \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \log{\left(x + \sqrt{x^{2} + 1} \right)} = \log{\left(1 + \sqrt{2} \right)}$$
More at x→1 from the right
Rapid solution [src] 
-oo
$$-\infty$$
Expand and simplify
The graph
Limit of the function log(x+sqrt(1+x^2))
    © Mister Exam – Calculator