The Taylor polynomial of degree 3 at $$\(x=0\)$$ for $$\((1+x)^{p}\)$$, where $$\(p\)$$ is a constant, is
A.
\(1+p x+p(p-1) x^{2}+p(p-1)(p-2) x^{3}\)
B.
\(1+p x+\frac{p(p-1)}{2} x^{2}+\frac{p(p-1)(p-2)}{3} x^{3}\)
C.
\(1+p x+\frac{p(p-1)}{2!} x^{2}+\frac{p(p-1)(p-2)}{3!} x^{3}\)
D.
\(p x+\frac{p(p-1)}{2!} x^{2}+\frac{p(p-1)(p-2)}{3!} x^{3}\)
Exam No：AP Calculus Unit 10 Questions Set Year：2024 Question No：34
Answer:
C
Knowledge points:
10.11 Finding Taylor Polynomial Approximations of Functions
10.14 Finding Taylor or Maclaurin Series for a Function
Solution:
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