Spring Semester 412
MATH-203
Differential & Integral Calculus
‫كلية الهندسة‬
‫بعنيزة‬
Unaizah College of Engineering
Tutorial Sheet- 04 (Maclaurin and Taylor Series; Power Series)
Problem-1: Find the Taylor series about x = x0 for the following function
(a) 𝑓(𝑥) = 𝑒
, 𝑥 = 2(b) 𝑓(𝑥) =
(c) 𝑓(𝑥) = ln (𝑥 + 1), 𝑥 = 1(d)
, 𝑥 =3
𝑓 (𝑥 ) = sin (𝑥 + 3), 𝑥 =
Problem-2: Find the Maclaurin series of the following function
(a)𝑒
(b)
(c) ln (𝑥 + 1)
(d)
sin (𝑥 + 3)
Problem-3: Find the interval of convergence of the following power series.
(a)
∑
(b)
∑
(c)
∑
(
)
( )
(
)
!