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1. Σ n! n=0 (-1)"x²n+1 2. ) 2n + 1 n=0 (-1)"x2n 3.) (2n)! n=0 x2n+1 4. (-1)"

1. Σ n! n=0 (-1)"x²n+1 2. ) 2n + 1 n=0 (-1)"x2n 3.) (2n)! n=0 x2n+1 4. (-1)"

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Match each of the Maclaurin series with the function it represents.
Here's a transcription of the image, featuring a series of infinite sums common in mathematical analysis: 1. The first series is: \[ \sum_{n=0}^{\infty} \frac{x^n}{n!} \] 2. The second series is: \[ \sum_{n=0}^{\infty} \frac{(-1)^n x^{2n+1}}{2n + 1} \] 3. The third series is: \[ \sum_{n=0}^{\infty} \frac{(-1)^n x^{2n}}{(2n)!} \] 4. The fourth series is: \[ \sum_{n=0}^{\infty} \frac{(-1)^n x^{2n+1}}{(2n + 1)!} \] These mathematical expressions represent different infinite series used in calculus and analysis, particularly for functions like exponential, sine, and cosine in their power series forms.
Transcribed Image Text:Here's a transcription of the image, featuring a series of infinite sums common in mathematical analysis: 1. The first series is: \[ \sum_{n=0}^{\infty} \frac{x^n}{n!} \] 2. The second series is: \[ \sum_{n=0}^{\infty} \frac{(-1)^n x^{2n+1}}{2n + 1} \] 3. The third series is: \[ \sum_{n=0}^{\infty} \frac{(-1)^n x^{2n}}{(2n)!} \] 4. The fourth series is: \[ \sum_{n=0}^{\infty} \frac{(-1)^n x^{2n+1}}{(2n + 1)!} \] These mathematical expressions represent different infinite series used in calculus and analysis, particularly for functions like exponential, sine, and cosine in their power series forms.
### Mathematical Functions The image contains a list of mathematical functions, labeled A through D, commonly used in calculus and trigonometry. Here they are: **A.** \( \text{arctan}(x) \) This is the inverse tangent function, which returns the angle whose tangent is \( x \). **B.** \( e^x \) This is the exponential function with base \( e \), where \( e \) is Euler's number, approximately equal to 2.71828. **C.** \( \sin(x) \) This is the sine function, which calculates the sine of an angle \( x \) and is a fundamental trigonometric function. **D.** \( \cos(x) \) This is the cosine function, which calculates the cosine of an angle \( x \), another fundamental trigonometric function. These functions are critical in various fields of mathematics and science, providing the foundations for understanding complex calculations and models.
Transcribed Image Text:### Mathematical Functions The image contains a list of mathematical functions, labeled A through D, commonly used in calculus and trigonometry. Here they are: **A.** \( \text{arctan}(x) \) This is the inverse tangent function, which returns the angle whose tangent is \( x \). **B.** \( e^x \) This is the exponential function with base \( e \), where \( e \) is Euler's number, approximately equal to 2.71828. **C.** \( \sin(x) \) This is the sine function, which calculates the sine of an angle \( x \) and is a fundamental trigonometric function. **D.** \( \cos(x) \) This is the cosine function, which calculates the cosine of an angle \( x \), another fundamental trigonometric function. These functions are critical in various fields of mathematics and science, providing the foundations for understanding complex calculations and models.
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