Formulas Assessment Flashcards
d/dx x^n
nx^n-1
d/dx constant
0
d/dx lnx
1/x
d/dx e^x
e^x
d/dx sinx
cos x
d/dx cos x
-sin x
d/dx a^x
a^x lna
d/dx log(base a) x
1/xlna
d/dx sec x
sec x tan x
d/dx cscx
-cscxcotx
d/dx tanx
sec^2x
d/dx cotx
-csc^2x
d/dx sin^-1x
1/√(1-x^2)
d/dx cos^-1x
-1/(√1-x^2)
d/dx tan^-1x
1/1+x^2d
d/dx (f(x)g(x))
f(x)g’(x) + f’(x)g(x)
d/dx (f(x)/g(x))
g(x)f’(x)-f(x)g’(x)/[g(x)]^2
d/dx (f(g(x)))
f’(g(x)) x g’(x)
∫ 1/x^n dx
x^-n+1/-n-1 +C
∫ x^n dx
x^n+1/n+1 +C
∫ a^x dx
a^x/ln a +C
∫ 1/x dx
ln |x| +C
∫ e^x dx
e^x +C
∫ csc^2x dx
-cotx +C
∫ sinx dx
-cos x +C
∫ cosx dx
sin x +C
∫ sec^2x dx
tanx +C
∫ secx tanx dx
secx +C
∫ cscx cotx dx
-cscx +C
∫ 1/√(1-x^2)dx
sin^-1x +C
∫ -1/√(1-x^2) dx
cos^-1x+C
∫ 1/1+x^2 dx
tan^-1x+c
∫ 1/x^2+a^2 dx
1/a tan^-1(x/a)+C
write the point slope form of a line
y=m(x-x1) +y1
how do we calculate displacement on (A,B) given a function, v(t)?
∫ A to B v(t) dt
How do we calculate speed given a function, v(t)?
|v(t)|
How do we find the distance between two curves f(x) and g(x) if f(x)>g(x)
f(x)-g(x)
How do we calculate total distance travelled on (A,B) given a function, v(t)?
∫ A to B |v(t)| dt
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
When finding the volume of solid given a cross sectional area, how do we calculate the bases length?
Base=Top Curve-Bottom Curve
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
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
