Mathematical Tool Flashcards
What is a function?
Relationship between 2 variables - dependent and independent [y = f(x)]
Domain and range ?
In [y = f(x)] All possible of x - domain, all possible value of y - range
In a linear function,f(x) = mx + c, slope and y intercept?
M = tan (theta) = slope , c - y intercept
X radian how many degrees?
X radian = 180/pi * x
X degrees = how many radians
X degrees = pi/180 * x radians
Sin 37, cos37 , tan37
3/5 , 4/5 , 3/4
Sin 53, cos 53, tan 53 ?
4/5 , 3/5, 4/3
C A S T rule
Revise from copy [NOW]
Sin(A+B)
SinA cosB +Cos A. Sin B
Sin (A-B)
Sin A cos B - Cos A sin B
Cos (A+B)
Cos A Cos B - sin A sin B
Cos (A - B)
Cos A Cos b + Sin A sin B
Tan (a+b)
tan a + tan B / 1- tan A tan B
Tan (a-b)
Tan A - tan B/ 1+tan A tan B
sin 2ø
2 Cosø sinø
cos 2ø
2 cos^2 ø - 1
cos ^ 2 ø =
1+cos 2ø/2
sin ^2 ø =
1-cos 2ø/2
f(ø) = A sinø + B cosø, then (f)max = ?
√a^2 + b^2
sine law? (side A opp to angle 1, side b opp to angle 2, side c = angle 3)
a/sin1 = b/sin2 = c/sin3
when ø is small then ø ≈ ?
ø ≈ tan ø ≈ sin ø
differentiation of y wrt x =
Lim ∆x –> 0 ∆y/∆x = dy/dx
secant in a curve is?
line joining any two points on a curve
tangent on a curve is ?
line just touching the curve, is a secant joining any nearby points.
y = 5, dy/dx = ?
0
y = mx, dy/dx = ?
m
y = x^n , dy/dx = ?
nx ^ n-1
d/dx(c x f(x)) = ?
C x d(f(x))/dx
d/dx(sinx) = ?
cos x
d/dx(cosx) = ?
-sinx
d/dx(e^x)
e^x
d/dx(lnx) = ?
1/x
d/dx[f(x) ± g(x)] = ?
d/dx(f(x)) ± d/dx(g(x))
(uv)’
multiplication rule?
u’v + v’u
read from copy
Trick f(x) = a , g(x) = b, u(x) = c
[a * b * c]’
from copy before quotient rule
a’ * b * c + a * b’ * c + a * b * c’
first differentiation of a, then b, then c
quotient rule
(u/v)’ = ?
vu’ - uv’/ v^2
read from notes
d/dx(tanx) = ?
sec^2 x
d/dx(cotx) = ?
-cosec^2 x
d/dx(secx) = ?
tan x . sec x
d/dx(cosecx) = ?
- cot x cosec x
chain rule
copy revision
dy^2/dx = ?
2y . dy/dx
dy^5 /dx = ?
5y^4 dy/dx
steps for point of maxima?
dy/dx = 0, d^2/dy = (-ve)
revise graph from copy
steps for point of minima?
dy/dx = 0, d^y/dx^2 = (+ve)
revise graph from copy
∫x^n dx = ?
x^n+1/n+1 + c
∫1/x dx = ?
lnx + c
∫sinx dx = ?
-cos x + c
∫cosx dx = ?
sinx + c
∫sec^2 x dx
tan x + c
∫tanx secx dx = ?
secx + c
∫ cot x cosec x = ?
-cosecx + c
∫cosec ^2 x dx = ?
-cot x + c
∫e^x dx = ?
e^x + c
∫lnx dx = ?
xlnx -x
∫ a^x dx = ?
a^x / lna
∫ {f(x) ± g(x)} dx = ?
addition rule
∫f(x) dx ± ∫g(x) dx
integration by substitution
read in copy
some more formulas
after substitution (there are so many)
read in copy
definite integration and average
read in copy
