Question

Find the Maclaurin series for the given function f(x) = e-6x ...


#20
Transcribed: Find the Maclaurin series for the given function f(x) = e-6x

Answer

The maclaurin series is:

 f(x)=f(0)+f^'(0)x+(f^('')(0))/(2!)x^2+(f^((3))(0))/(3!)x^3+...+(f^((n))(0))/(n!)x^n+....

f(x)=e-6x     ,    f(0)=1f'(x)=-6e-6x     ,    f'(0)=-6(1)=-6f''(x)=36e-6x     ,    f''(0)=36(1)=36f'''(x)=-216e-6x     ,    f'''(0)=-6(1)=-216f''''(x)=1296e-6x     ,    f''''(0)=1296(1)=1296

so,f(x)=1-6x+362!x2-2163!x3+12964!x4+....

      

 

The maclaurin series of f(x)=e-6x is:

f(x)=1-6x+362!x2-2163!x3+12964!x4+....

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