The document contains mathematical expressions including: 1) The Taylor series expansion for the exponential function e^x; 2) Trigonometric identities for sums of cosines; 3) The Fourier series representation of a function f(x).

1. 𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
cos 𝛼 + cos 𝛽 = 2 cos
1
2
𝛼 + 𝛽 cos
1
2
𝛼 − 𝛽
𝑒 𝑥 = 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
+ ⋯ , −∞ < 𝑥 < ∞
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
cos 𝛼 + cos 𝛽 = 2 cos
1
2
𝛼 + 𝛽 cos
1
2
𝛼 − 𝛽
𝑒 𝑥
= 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
+ ⋯ , −∞ < 𝑥 < ∞
𝑒 𝑥
= 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
∞
𝑎2
+ 𝑏2
= 𝑐2
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑓 𝑥 = 𝑎0 +
𝑛=1
∞
𝑎 𝑛 cos
𝑛𝜋𝑥
𝐿
+ 𝑏 𝑛 sin
𝑛𝜋𝑥
𝐿
𝑒 𝑥
= 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
+ ⋯ , −∞ < 𝑥 < ∞
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑥 =
−𝑏 ± 𝑏2 − 4𝑎𝑐
2𝑎
𝑎2
+ 𝑏2
= 𝑐2
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑓 𝑥 = 𝑎0 +
𝑛=1
∞
𝑎 𝑛 cos
𝑛𝜋𝑥
𝐿
+ 𝑏 𝑛 sin
𝑛𝜋𝑥
𝐿
𝑒 𝑥 = 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
+ ⋯ , −∞ < 𝑥 < ∞
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑥 =
−𝑏 ± 𝑏2 − 4𝑎𝑐
2𝑎
𝑎2
+ 𝑏2
= 𝑐2
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑎2
+ 𝑏2
= 𝑐2
cos 𝛼 + cos 𝛽 = 2 cos
1
2
𝛼 + 𝛽 cos
1
2
𝛼 − 𝛽
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑒 𝑥
= 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
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3. 𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
cos 𝛼 + cos 𝛽 = 2 cos
1
2
𝛼 + 𝛽 cos
1
2
𝛼 − 𝛽
𝑒 𝑥 = 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
+ ⋯ , −∞ < 𝑥 < ∞
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
cos 𝛼 + cos 𝛽 = 2 cos
1
2
𝛼 + 𝛽 cos
1
2
𝛼 − 𝛽
𝑒 𝑥
= 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
+ ⋯ , −∞ < 𝑥 < ∞
𝑒 𝑥
= 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
∞
𝑎2
+ 𝑏2
= 𝑐2
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑓 𝑥 = 𝑎0 +
𝑛=1
∞
𝑎 𝑛 cos
𝑛𝜋𝑥
𝐿
+ 𝑏 𝑛 sin
𝑛𝜋𝑥
𝐿
𝑒 𝑥
= 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
+ ⋯ , −∞ < 𝑥 < ∞
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑥 =
−𝑏 ± 𝑏2 − 4𝑎𝑐
2𝑎
𝑎2
+ 𝑏2
= 𝑐2
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑓 𝑥 = 𝑎0 +
𝑛=1
∞
𝑎 𝑛 cos
𝑛𝜋𝑥
𝐿
+ 𝑏 𝑛 sin
𝑛𝜋𝑥
𝐿
𝑒 𝑥 = 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
+ ⋯ , −∞ < 𝑥 < ∞
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑥 =
−𝑏 ± 𝑏2 − 4𝑎𝑐
2𝑎
𝑎2
+ 𝑏2
= 𝑐2
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑎2
+ 𝑏2
= 𝑐2
cos 𝛼 + cos 𝛽 = 2 cos
1
2
𝛼 + 𝛽 cos
1
2
𝛼 − 𝛽
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑒 𝑥
= 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
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4. 𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
cos 𝛼 + cos 𝛽 = 2 cos
1
2
𝛼 + 𝛽 cos
1
2
𝛼 − 𝛽
𝑒 𝑥 = 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
+ ⋯ , −∞ < 𝑥 < ∞
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
cos 𝛼 + cos 𝛽 = 2 cos
1
2
𝛼 + 𝛽 cos
1
2
𝛼 − 𝛽
𝑒 𝑥
= 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
+ ⋯ , −∞ < 𝑥 < ∞
𝑒 𝑥
= 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
∞
𝑎2
+ 𝑏2
= 𝑐2
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑓 𝑥 = 𝑎0 +
𝑛=1
∞
𝑎 𝑛 cos
𝑛𝜋𝑥
𝐿
+ 𝑏 𝑛 sin
𝑛𝜋𝑥
𝐿
𝑒 𝑥
= 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
+ ⋯ , −∞ < 𝑥 < ∞
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑥 =
−𝑏 ± 𝑏2 − 4𝑎𝑐
2𝑎
𝑎2
+ 𝑏2
= 𝑐2
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑓 𝑥 = 𝑎0 +
𝑛=1
∞
𝑎 𝑛 cos
𝑛𝜋𝑥
𝐿
+ 𝑏 𝑛 sin
𝑛𝜋𝑥
𝐿
𝑒 𝑥 = 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
+ ⋯ , −∞ < 𝑥 < ∞
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑥 =
−𝑏 ± 𝑏2 − 4𝑎𝑐
2𝑎
𝑎2
+ 𝑏2
= 𝑐2
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑎2
+ 𝑏2
= 𝑐2
cos 𝛼 + cos 𝛽 = 2 cos
1
2
𝛼 + 𝛽 cos
1
2
𝛼 − 𝛽
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑒 𝑥
= 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
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6. 𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
cos 𝛼 + cos 𝛽 = 2 cos
1
2
𝛼 + 𝛽 cos
1
2
𝛼 − 𝛽
𝑒 𝑥 = 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
+ ⋯ , −∞ < 𝑥 < ∞
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
cos 𝛼 + cos 𝛽 = 2 cos
1
2
𝛼 + 𝛽 cos
1
2
𝛼 − 𝛽
𝑒 𝑥
= 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
+ ⋯ , −∞ < 𝑥 < ∞
𝑒 𝑥
= 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
∞
𝑎2
+ 𝑏2
= 𝑐2
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑓 𝑥 = 𝑎0 +
𝑛=1
∞
𝑎 𝑛 cos
𝑛𝜋𝑥
𝐿
+ 𝑏 𝑛 sin
𝑛𝜋𝑥
𝐿
𝑒 𝑥
= 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
+ ⋯ , −∞ < 𝑥 < ∞
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑥 =
−𝑏 ± 𝑏2 − 4𝑎𝑐
2𝑎
𝑎2
+ 𝑏2
= 𝑐2
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑓 𝑥 = 𝑎0 +
𝑛=1
∞
𝑎 𝑛 cos
𝑛𝜋𝑥
𝐿
+ 𝑏 𝑛 sin
𝑛𝜋𝑥
𝐿
𝑒 𝑥 = 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
+ ⋯ , −∞ < 𝑥 < ∞
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑥 =
−𝑏 ± 𝑏2 − 4𝑎𝑐
2𝑎
𝑎2
+ 𝑏2
= 𝑐2
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑎2
+ 𝑏2
= 𝑐2
cos 𝛼 + cos 𝛽 = 2 cos
1
2
𝛼 + 𝛽 cos
1
2
𝛼 − 𝛽
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑒 𝑥
= 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
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7. 𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
cos 𝛼 + cos 𝛽 = 2 cos
1
2
𝛼 + 𝛽 cos
1
2
𝛼 − 𝛽
𝑒 𝑥 = 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
+ ⋯ , −∞ < 𝑥 < ∞
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
cos 𝛼 + cos 𝛽 = 2 cos
1
2
𝛼 + 𝛽 cos
1
2
𝛼 − 𝛽
𝑒 𝑥
= 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
+ ⋯ , −∞ < 𝑥 < ∞
𝑒 𝑥
= 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
∞
𝑎2
+ 𝑏2
= 𝑐2
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑓 𝑥 = 𝑎0 +
𝑛=1
∞
𝑎 𝑛 cos
𝑛𝜋𝑥
𝐿
+ 𝑏 𝑛 sin
𝑛𝜋𝑥
𝐿
𝑒 𝑥
= 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
+ ⋯ , −∞ < 𝑥 < ∞
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑥 =
−𝑏 ± 𝑏2 − 4𝑎𝑐
2𝑎
𝑎2
+ 𝑏2
= 𝑐2
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑓 𝑥 = 𝑎0 +
𝑛=1
∞
𝑎 𝑛 cos
𝑛𝜋𝑥
𝐿
+ 𝑏 𝑛 sin
𝑛𝜋𝑥
𝐿
𝑒 𝑥 = 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
+ ⋯ , −∞ < 𝑥 < ∞
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑥 =
−𝑏 ± 𝑏2 − 4𝑎𝑐
2𝑎
𝑎2
+ 𝑏2
= 𝑐2
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑎2
+ 𝑏2
= 𝑐2
cos 𝛼 + cos 𝛽 = 2 cos
1
2
𝛼 + 𝛽 cos
1
2
𝛼 − 𝛽
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑒 𝑥
= 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
1.Tap Classroom .
2.Tap the class Classwork .
3.At the top right, tap Your work .
To see details for an assignment, tap the assignment title.
4.(Optional) To filter your work, tap Filter and choose an
option: Assigned, Returned with grade, or Missing.
To see more details, tap the title of the work.
.

8. 𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
cos 𝛼 + cos 𝛽 = 2 cos
1
2
𝛼 + 𝛽 cos
1
2
𝛼 − 𝛽
𝑒 𝑥 = 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
+ ⋯ , −∞ < 𝑥 < ∞
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
cos 𝛼 + cos 𝛽 = 2 cos
1
2
𝛼 + 𝛽 cos
1
2
𝛼 − 𝛽
𝑒 𝑥
= 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
+ ⋯ , −∞ < 𝑥 < ∞
𝑒 𝑥
= 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
∞
𝑎2
+ 𝑏2
= 𝑐2
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑓 𝑥 = 𝑎0 +
𝑛=1
∞
𝑎 𝑛 cos
𝑛𝜋𝑥
𝐿
+ 𝑏 𝑛 sin
𝑛𝜋𝑥
𝐿
𝑒 𝑥
= 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
+ ⋯ , −∞ < 𝑥 < ∞
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑥 =
−𝑏 ± 𝑏2 − 4𝑎𝑐
2𝑎
𝑎2
+ 𝑏2
= 𝑐2
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑓 𝑥 = 𝑎0 +
𝑛=1
∞
𝑎 𝑛 cos
𝑛𝜋𝑥
𝐿
+ 𝑏 𝑛 sin
𝑛𝜋𝑥
𝐿
𝑒 𝑥 = 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
+ ⋯ , −∞ < 𝑥 < ∞
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑥 =
−𝑏 ± 𝑏2 − 4𝑎𝑐
2𝑎
𝑎2
+ 𝑏2
= 𝑐2
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑎2
+ 𝑏2
= 𝑐2
cos 𝛼 + cos 𝛽 = 2 cos
1
2
𝛼 + 𝛽 cos
1
2
𝛼 − 𝛽
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑒 𝑥
= 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
Filter work by class
On the To-do page, you'll find work filtered by class,
and see work that’s:
To-do—Work assigned and not yet completed. You’ll
see the class and work titles grouped as missing, no
due date, due today or within the week, or later.
Done—Work you completed and turned in. You’ll see
the status of the work—turned in or done late—and
grades if the work is graded.

9. 𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
cos 𝛼 + cos 𝛽 = 2 cos
1
2
𝛼 + 𝛽 cos
1
2
𝛼 − 𝛽
𝑒 𝑥 = 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
+ ⋯ , −∞ < 𝑥 < ∞
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
cos 𝛼 + cos 𝛽 = 2 cos
1
2
𝛼 + 𝛽 cos
1
2
𝛼 − 𝛽
𝑒 𝑥
= 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
+ ⋯ , −∞ < 𝑥 < ∞
𝑒 𝑥
= 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
∞
𝑎2
+ 𝑏2
= 𝑐2
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑓 𝑥 = 𝑎0 +
𝑛=1
∞
𝑎 𝑛 cos
𝑛𝜋𝑥
𝐿
+ 𝑏 𝑛 sin
𝑛𝜋𝑥
𝐿
𝑒 𝑥
= 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
+ ⋯ , −∞ < 𝑥 < ∞
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑥 =
−𝑏 ± 𝑏2 − 4𝑎𝑐
2𝑎
𝑎2
+ 𝑏2
= 𝑐2
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑓 𝑥 = 𝑎0 +
𝑛=1
∞
𝑎 𝑛 cos
𝑛𝜋𝑥
𝐿
+ 𝑏 𝑛 sin
𝑛𝜋𝑥
𝐿
𝑒 𝑥 = 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
+ ⋯ , −∞ < 𝑥 < ∞
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑥 =
−𝑏 ± 𝑏2 − 4𝑎𝑐
2𝑎
𝑎2
+ 𝑏2
= 𝑐2
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑎2
+ 𝑏2
= 𝑐2
cos 𝛼 + cos 𝛽 = 2 cos
1
2
𝛼 + 𝛽 cos
1
2
𝛼 − 𝛽
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑒 𝑥
= 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
See the latest work and announcements
You can see the latest work and
announcements on the Stream page. The
most recent post is always at the top.
1.Tap Classroom .
2.Tap the class.
3.(Optional) To see any instructions or
feedback, tap the assignment or question.

10. 𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
cos 𝛼 + cos 𝛽 = 2 cos
1
2
𝛼 + 𝛽 cos
1
2
𝛼 − 𝛽
𝑒 𝑥 = 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
+ ⋯ , −∞ < 𝑥 < ∞
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
cos 𝛼 + cos 𝛽 = 2 cos
1
2
𝛼 + 𝛽 cos
1
2
𝛼 − 𝛽
𝑒 𝑥
= 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
+ ⋯ , −∞ < 𝑥 < ∞
𝑒 𝑥
= 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
∞
𝑎2
+ 𝑏2
= 𝑐2
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑓 𝑥 = 𝑎0 +
𝑛=1
∞
𝑎 𝑛 cos
𝑛𝜋𝑥
𝐿
+ 𝑏 𝑛 sin
𝑛𝜋𝑥
𝐿
𝑒 𝑥
= 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
+ ⋯ , −∞ < 𝑥 < ∞
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑥 =
−𝑏 ± 𝑏2 − 4𝑎𝑐
2𝑎
𝑎2
+ 𝑏2
= 𝑐2
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑓 𝑥 = 𝑎0 +
𝑛=1
∞
𝑎 𝑛 cos
𝑛𝜋𝑥
𝐿
+ 𝑏 𝑛 sin
𝑛𝜋𝑥
𝐿
𝑒 𝑥 = 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
+ ⋯ , −∞ < 𝑥 < ∞
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑥 =
−𝑏 ± 𝑏2 − 4𝑎𝑐
2𝑎
𝑎2
+ 𝑏2
= 𝑐2
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑎2
+ 𝑏2
= 𝑐2
cos 𝛼 + cos 𝛽 = 2 cos
1
2
𝛼 + 𝛽 cos
1
2
𝛼 − 𝛽
𝑥 + 𝑎 𝑛
=
𝑘=0
𝑛
𝑛
𝑘
𝑥 𝑘
𝑎 𝑛−𝑘
𝑒 𝑥
= 1 +
𝑥
1!
+
𝑥2
2!
+
𝑥3
3!
Thanks
Teacher Mona Youssef