Download FORMULA SHEET FOR MAT187 Trigonometric Identities. • cos 2(x

FORMULA SHEET FOR MAT187
Trigonometric Identities.
• cos2 (x) =
1 + cos(2x)
2
• sin2 (x) =
1 − cos(2x)
2
• sin(x) = cos
π
2
−x
Applications of integration.
Z bq
2
1 + f 0 (x) dx
• Arc length for y = f (x)
a
Z
• Area of a surface of revolution y = f (x) revolved around x−axis
b
2πf (x)
q
2
1 + f 0 (x) dx
a
• Hyperbolic Functions

x
−x

 sinh(x) = e − e
2 −x
x

 cosh(x) = e + e
2
Sequences.
• Important limit
lim
n→∞
n
X
• Geometric Sum
1+
a n
= ea
n
xk =
1 − xn+1
1−x
k=0
Power Series.
• Taylor Theorem
• Taylor Series


f (x) = pn (x) + Rn (x)



n

X

f (k) (a)

(x − a)k
pn (x) =
k!

k=0



f (n+1) (c)


(x − a)n+1
 Rn (x) =
(n + 1)!
f (x) =
∞
X
f (k) (a)
k=0
• Taylor Series for f (x) = sin x
k!
(x − a)k
∞
X
(−1)k 2k+1
x
(2k + 1)!
k=0
• Taylor Series for f (x) = cos x
∞
X
(−1)k
k=0
• Taylor Series for f (x) = ln(1 − x)
(2k)!
x2k
∞
X
1 k
−
x
k
k=1