Calculus Examples

Find the Domain arcsin(e^x)
Step 1
Set the argument in greater than or equal to to find where the expression is defined.
Step 2
Solve for .
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Step 2.1
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Step 2.2
The equation cannot be solved because is undefined.
Undefined
Step 2.3
There is no solution for
No solution
No solution
Step 3
Set the argument in less than or equal to to find where the expression is defined.
Step 4
Solve for .
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Step 4.1
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Step 4.2
Expand the left side.
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Step 4.2.1
Expand by moving outside the logarithm.
Step 4.2.2
The natural logarithm of is .
Step 4.2.3
Multiply by .
Step 4.3
The natural logarithm of is .
Step 5
The domain is all values of that make the expression defined.
Interval Notation:
Set-Builder Notation:
Step 6