Consider the following function,
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Answer:
Step-by-step explanation:
Rn(x) →0
f(x) = 10/x
a = -2
Taylor series for the function <em>f </em>at the number a is:
............ equation (1)
Now we will find the function <em>f </em> and all derivatives of the function <em>f</em> at a = -2
f(x) = 10/x f(-2) = 10/-2
f'(x) = -10/x² f'(-2) = -10/(-2)²
f"(x) = -10.2/x³ f"(-2) = -10.2/(-2)³
f"'(x) = -10.2.3/x⁴ f'"(-2) = -10.2.3/(-2)⁴
f""(x) = -10.2.3.4/x⁵ f""(-2) = -10.2.3.4/(-2)⁵
∴ The Taylor series for the function <em>f</em> at a = -4 means that we substitute the value of each function into equation (1)
So, we get Or