E calculator Eeraised to Power of X
Our free exponents & logarithms calculator solves ecalculator eeraised power problems. Get worked examples, visual aids, and downloadable results.
Formula
e^x = 1 + x + x^2/2! + x^3/3! + ... (Taylor series)
The exponential function e^x where e is Euler's number (approximately 2.71828). It can be computed via the Taylor series which converges for all real x. The function is its own derivative and integral, making it fundamental in calculus.
Worked Examples
Example 1: Computing e^2 with Taylor Series
Problem: Calculate e^2 and verify using the Taylor series expansion to 6 terms.
Solution: e^2 = 7.389056...\n\nTaylor series: e^x = 1 + x + x^2/2! + x^3/3! + x^4/4! + x^5/5!\nFor x = 2:\nTerm 0: 1\nTerm 1: 2\nTerm 2: 4/2 = 2\nTerm 3: 8/6 = 1.3333\nTerm 4: 16/24 = 0.6667\nTerm 5: 32/120 = 0.2667\nPartial sum = 7.2667 (error = 0.1224)
Result: e^2 = 7.389056 | 6-term approximation = 7.2667 (98.3% accurate)
Example 2: Continuous Compounding
Problem: Find the value of $5,000 invested at 8% for 10 years with continuous compounding using A = P*e^(rt).
Solution: A = P * e^(rt)\nA = 5000 * e^(0.08 * 10)\nA = 5000 * e^(0.8)\ne^(0.8) = 2.2255\nA = 5000 * 2.2255 = $11,127.70\n\nInterest earned: $11,127.70 - $5,000 = $6,127.70
Result: A = $11,127.70 | Interest earned = $6,127.70
Frequently Asked Questions
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All calculations use established mathematical formulas and are performed with high-precision arithmetic. Results are accurate to the precision shown. For critical decisions in finance, medicine, or engineering, always verify results with a qualified professional.
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What formula does E calculator Eeraised to Power of X use?
The formula used is described in the Formula section on this page. It is based on widely accepted standards in the relevant field. If you need a specific reference or citation, the References section provides links to authoritative sources.
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