Sum of the series and recurrence relationship.
When they tell you to find f(x) from a differentiated expression:
1. Integrate the expression
2. Substitute the numbers of the given point to find C.
3. Add the value of C to your integrated equation.
When they say find the normal to C at a given point:
1. Differentiate the expression.
2. Substitute the numers in to find M
3. As the gradient of the normal is -1/M, do this and use the equation
y-y1=m(x-x1) along with the coordinates given.
Proving the sum of the series
Translations and transformations of graphs:
Translations and transformations:
f(x-a)= move a to left
f(x+a)= move a to right
f(x)+a= move a upwards.
f(ax)= multiply x coordinates by 1/a
af(x)= multiply y coordinates by a
f(-x)= the graph reflect on the Y AXIS
-f(x)= the graph reflects on the X AXIS
Coordinate geometry formulae:
the gradient of a perpendicular line is -1/m
the normal to a line is perpendicular to the tangent
Use pythagoras to find the distance between two points.
Indices& other rules
When you get a fractional indice REMEMBER to first do the square/cubed/etc. root and then multiply it by the power given.
Anything to the power of 0= 1
Integrate the following expression x^n --->>> x^n+1/n+1
Differentiate the following expression: ax^n --->>> n(ax)^n-1
Completing the square:
Even if you have extra numbers that aren't part of B just add them to the general equation!
When using inequality signs, you need to know which part of the graph they're looking for.
1. If 2x+3y+1<0, they're looking for the inside region- the part of the curve under the x-axis.
2. If 2x+3y+1>0, they're looking for the outside region- the part of the curve which is above the x-axis.