Question

Finding Taylor Series Use substitution (as in Formula (7)) to find the Taylor series at \( x=0 \) of the functions in Exercises 1-12. 1. \( e^{-5 x} \) 2. \( e^{-x / 2} \) 3. \( 5 \sin (-x) \) 4. \( \sin \left(\frac{\pi x}{2}\right) \) 5. \( \cos 5 x^{2} \) 6. \( \cos (x / \sqrt{2}) \) 7. \( \ln \left(1+x^{2}\right) \) 8. \( \tan ^{-1}\left(3 x^{4}\right) \) 9. \( \frac{1}{1+\frac{3}{4} x^{3}} \) 10. \( \frac{1}{2-x} \) 11. \( \ln (3+6 x) \) 12. \( e^{-x^{2}+\ln 5} \)

          Finding Taylor Series
Use substitution (as in Formula (7)) to find the Taylor series at \( x=0 \) of the functions in Exercises 1-12.
1. \( e^{-5 x} \)
2. \( e^{-x / 2} \)
3. \( 5 \sin (-x) \)
4. \( \sin \left(\frac{\pi x}{2}\right) \)
5. \( \cos 5 x^{2} \)
6. \( \cos (x / \sqrt{2}) \)
7. \( \ln \left(1+x^{2}\right) \)
8. \( \tan ^{-1}\left(3 x^{4}\right) \)
9. \( \frac{1}{1+\frac{3}{4} x^{3}} \)
10. \( \frac{1}{2-x} \)
11. \( \ln (3+6 x) \)
12. \( e^{-x^{2}+\ln 5} \)

Finding Taylor Series
Use substitution (as in Formula (7)) to find the Taylor series at x=0 of the functions in Exercises 1-12.
1. e^-5 x
2. e^-x / 2
3. 5 sin (-x)
4. sin((π x)/(2))
5. cos 5 x^2
6. cos (x / √(2))
7. ln(1+x^2)
8. tan ^-1(3 x^4)
9. (1)/(1+(3)/(4) x^3)
10. (1)/(2-x)
11. ln (3+6 x)
12. e^-x^2+ln 5

Added by Xavier Y.

University Calculus: Early Transcendentals

Joel Hass, Christopher Heil, Przemyslaw… 4th Edition

Chapter 9

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Finding Taylor Series Use substitution (as in Formula (7)) to find the Taylor series at \( x=0 \) of the functions in Exercises 1-12. 1. \( e^{-5 x} \) 2. \( e^{-x / 2} \) 3. \( 5 \sin (-x) \) 4. \( \sin \left(\frac{\pi x}{2}\right) \) 5. \( \cos 5 x^{2} \) 6. \( \cos (x / \sqrt{2}) \) 7. \( \ln \left(1+x^{2}\right) \) 8. \( \tan ^{-1}\left(3 x^{4}\right) \) 9. \( \frac{1}{1+\frac{3}{4} x^{3}} \) 10. \( \frac{1}{2-x} \) 11. \( \ln (3+6 x) \) 12. \( e^{-x^{2}+\ln 5} \)