Calculus Examples

Graph natural log of x^2+1
Step 1
Find the asymptotes.
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Step 1.1
Set the argument of the logarithm equal to zero.
Step 1.2
Solve for .
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Step 1.2.1
Subtract from both sides of the equation.
Step 1.2.2
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 1.2.3
Rewrite as .
Step 1.2.4
The complete solution is the result of both the positive and negative portions of the solution.
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Step 1.2.4.1
First, use the positive value of the to find the first solution.
Step 1.2.4.2
Next, use the negative value of the to find the second solution.
Step 1.2.4.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 1.3
The vertical asymptote occurs at .
Vertical Asymptote:
Vertical Asymptote:
Step 2
Find the point at .
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Step 2.1
Replace the variable with in the expression.
Step 2.2
Simplify the result.
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Step 2.2.1
One to any power is one.
Step 2.2.2
Add and .
Step 2.2.3
The final answer is .
Step 2.3
Convert to decimal.
Step 3
Find the point at .
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Step 3.1
Replace the variable with in the expression.
Step 3.2
Simplify the result.
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Step 3.2.1
Raise to the power of .
Step 3.2.2
Add and .
Step 3.2.3
The final answer is .
Step 3.3
Convert to decimal.
Step 4
Find the point at .
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Step 4.1
Replace the variable with in the expression.
Step 4.2
Simplify the result.
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Step 4.2.1
Raise to the power of .
Step 4.2.2
Add and .
Step 4.2.3
The final answer is .
Step 4.3
Convert to decimal.
Step 5
The log function can be graphed using the vertical asymptote at and the points .
Vertical Asymptote:
Step 6