ams 161 trig identies midterm 2

d/dx tan(x)

sec²(x)

d/dx cot(x)

-csc²(x)

sin²x + cos²x

1

tan²x + 1

sec²x

sin(2x)

2(sinx * cos x)

cos(2x)

2cos²x - 1

d/dx (sec x)

sec (x) * tan(x)

divergent test

lim_{n → ∞} b_n = DNE, or ≠ 0 - series diverges

lim_{n → ∞} b_n = 0 - inconclusive

alternating estimation theorem

|S - S_n| ≤ b_n + 1

*can only be used when series passes AST

alternating series test

if ∑(-1)ⁿ * b_n

b_n is decreasing

lim_{n → ∞} b_n = 0

then series converges

absolute ratio test

lim_{n → ∞} (b_{n + 1} * (1/b_n))

integration by parts

∫u dv = uv - ∫v du