Calculus Examples

Find the Domain square root of 1-2^t
Step 1
Set the radicand in greater than or equal to to find where the expression is defined.
Step 2
Solve for .
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Step 2.1
Subtract from both sides of the inequality.
Step 2.2
Divide each term in by and simplify.
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Step 2.2.1
Divide each term in by . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.
Step 2.2.2
Simplify the left side.
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Step 2.2.2.1
Dividing two negative values results in a positive value.
Step 2.2.2.2
Divide by .
Step 2.2.3
Simplify the right side.
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Step 2.2.3.1
Divide by .
Step 2.3
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Step 2.4
Expand by moving outside the logarithm.
Step 2.5
Simplify the right side.
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Step 2.5.1
The natural logarithm of is .
Step 2.6
Divide each term in by and simplify.
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Step 2.6.1
Divide each term in by .
Step 2.6.2
Simplify the left side.
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Step 2.6.2.1
Cancel the common factor of .
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Step 2.6.2.1.1
Cancel the common factor.
Step 2.6.2.1.2
Divide by .
Step 2.6.3
Simplify the right side.
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Step 2.6.3.1
Divide by .
Step 3
The domain is all values of that make the expression defined.
Interval Notation:
Set-Builder Notation:
Step 4