5. Find the Taylor series expansion for the function f(x) = sinh x around x = 0 (Commonly called the MacLaurin series for sinh x). After you find the series, use the Ratio test to determine the radius of convergence f(x) = sinx f'(x) f"(x) = f""(x) = f(4)(x) = f(0) = f'(0) = f"(0) = f(0) = f(4)(x) = Therefore the MacLaurin series expansion for f(x) = sinh x is Radius of convergence: Co = C₁ = C₂ = C3 =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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5. Find the Taylor series expansion for the function f(x) = sinh x around x = 0 (Commonly called the MacLaurin series
for sinh x). After you find the series, use the Ratio test to determine the radius of convergence
f(x) = sinx
f'(x)
f"(x) =
f""(x) =
f(¹)(x) =
f(0) =
f'(0) =
f"(0) =
f(0) =
f(4) (x)
Therefore the MacLaurin series expansion for f(x) = sinh x is
Radius of convergence:
=
Co=
C₁ =
C₂ =
C3 =
C4 =
Transcribed Image Text:5. Find the Taylor series expansion for the function f(x) = sinh x around x = 0 (Commonly called the MacLaurin series for sinh x). After you find the series, use the Ratio test to determine the radius of convergence f(x) = sinx f'(x) f"(x) = f""(x) = f(¹)(x) = f(0) = f'(0) = f"(0) = f(0) = f(4) (x) Therefore the MacLaurin series expansion for f(x) = sinh x is Radius of convergence: = Co= C₁ = C₂ = C3 = C4 =
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