Formulas Assessment Flashcards
1
Q
d/dx x^n
A
nx^n-1
2
Q
d/dx constant
A
0
3
Q
d/dx lnx
A
1/x
4
Q
d/dx e^x
A
e^x
5
Q
d/dx sinx
A
cos x
6
Q
d/dx cos x
A
-sin x
7
Q
d/dx a^x
A
a^x lna
8
Q
d/dx log(base a) x
A
1/xlna
9
Q
d/dx sec x
A
sec x tan x
10
Q
d/dx cscx
A
-cscxcotx
11
Q
d/dx tanx
A
sec^2x
12
Q
d/dx cotx
A
-csc^2x
13
Q
d/dx sin^-1x
A
1/√(1-x^2)
14
Q
d/dx cos^-1x
A
-1/(√1-x^2)
15
Q
d/dx tan^-1x
A
1/1+x^2d
16
Q
d/dx (f(x)g(x))
A
f(x)g’(x) + f’(x)g(x)
17
Q
d/dx (f(x)/g(x))
A
g(x)f’(x)-f(x)g’(x)/[g(x)]^2
18
Q
d/dx (f(g(x)))
A
f’(g(x)) x g’(x)
19
Q
∫ 1/x^n dx
A
x^-n+1/-n-1 +C
20
Q
∫ x^n dx
A
x^n+1/n+1 +C
21
Q
∫ a^x dx
A
a^x/ln a +C
22
Q
∫ 1/x dx
A
ln |x| +C
23
Q
∫ e^x dx
A
e^x +C
24
Q
∫ csc^2x dx
A
-cotx +C
25
∫ sinx dx
-cos x +C
26
∫ cosx dx
sin x +C
27
∫ sec^2x dx
tanx +C
28
∫ secx tanx dx
secx +C
29
∫ cscx cotx dx
-cscx +C
30
∫ 1/√(1-x^2)dx
sin^-1x +C
31
∫ -1/√(1-x^2) dx
cos^-1x+C
32
∫ 1/1+x^2 dx
tan^-1x+c
33
∫ 1/x^2+a^2 dx
1/a tan^-1(x/a)+C
34
write the point slope form of a line
y=m(x-x1) +y1
35
how do we calculate displacement on (A,B) given a function, v(t)?
∫ A to B v(t) dt
36
How do we calculate speed given a function, v(t)?
|v(t)|
37
How do we find the distance between two curves f(x) and g(x) if f(x)>g(x)
f(x)-g(x)
38
How do we calculate total distance travelled on (A,B) given a function, v(t)?
∫ A to B |v(t)| dt
39
How do we find the bounds of an integral involving area or volume of two functions f(x) and g(x) if they are not given?
Setting f(x) = g(x) and solving for x
40
When finding the volume of solid given a cross sectional area, how do we calculate the bases length?
Base=Top Curve-Bottom Curve
41
How do we find the volume formed by rotating f(x) around the line y=k on (A,B)?
∫ A to B π(f(x)-k)^2 dx
42
How do we find the area between two curves f(x) and g(x) on (A,B) is f(x)>g(x)?
∫A to B [f(x)-g(x)] dx
