Calc 213 Flashcards
1
Q
d/dx sinx
A
cosx
2
Q
d/dx cosx
A
-sinx
3
Q
d/dx tanx
A
sec2x
4
Q
d/dx cotx
A
- csc2x
5
Q
d/dx sec x
A
sec x tan x
6
Q
d/dx csc x
A
-csc x cot x
7
Q
∫ sin x dx
A
- cos x + C
8
Q
∫ cos x dx
A
sin x + C
9
Q
∫ sec2 x dx
A
tan x + C
10
Q
∫ csc2 x dx
A
- cot x + C
11
Q
∫sec x tan x dx
A
sec x + C
12
Q
∫csc x cot x dx
A
- csc x + C
13
Q
lim x -> a [f(x) +/- g(x)]
A
lim x -> a f(x) +/- lim x -> a g(x)
14
Q
lim x -> a [f(x) * g(x)]
A
lim x -> a f(x) * lim x -> a g(x)
15
Q
lim x -> a p(x)
(p = polynomial)
A
p(a)
16
Q
If f(x) = g(x)
A
the limits of the functions are equal for all when “x” does not equal “a”
17
Q
d/dx [ag(x)]
A
(ln a)*ag(x)*g’(x)
18
Q
Trapezoidal Rule
A
∫abf(x) dx ≈ ((b-a)/n) [1/2 f(x0) + f(x1)… + 1/2f(xn)]
19
Q
Simpson’s Rule
A
∫abf(x) dx ≈
((b-a)/3n) [f(x0) +4f(x1)+ 2f(x2) … + f(xn)]
20
Q
∫ u dv
A
uv - ∫ v du
