Vectors & Geometry
Magnitude of v = 3i + 4j
5
Equation of a straight line through points (0,0) and (2,3)
y = 3/2 x
Solve e^x = 5
x = ln(5)
Derivative of x^3
3x^2
Derivative of sin x
cos x
Multiply v = i + j by scalar 3
3i + 3j
Condition for two lines to be parallel
Gradient/Slopes are equal
Solve 2^x = 8
x = 3
Derivative of e^x
e^x
Find dy/dx if y = x^2 + 3x + 1
dy/dx = 2x + 3
Midpoint of A(1,2) and B(5,6)
(3,4)
Equation of circle with center (2, -3) and radius 5
(x-2)^2 + (y+3)^2 = 25
Simplify log_a (xy)
log_a x + log_a y
Find stationary points of f(x) = x^3 - 3x^2 + 2
f'(x) = 3x^2 - 6x = 3x(x-2), stationary points at x = 0, 2
Use first derivative test to determine max/min of f(x) = -x^2 + 4x + 1
Maximum at x = 2
Length of line segment AB with A(0,0) and B(3,4)
5
Find intersection points of x^2 + y^2 = 5 and y = x + 1
(1,2), (-2,-1)
Change of base formula for log_b x
log_b x = log x / log b
Integrate x^2 dx
x^3 / 3 + C
Integrate e^(2x) dx
(1/2) e^(2x) + C
Equation of perpendicular bisector of AB with A(0,0), B(2,4)
y = -x + 2
Find tangent to circle x^2 + y^2 = 4 at point (2,0)
x = 2
Find displacement s if v = ds/dt = 3t^2, initial s=0
s = t^3
Solve dx/dt = 5, x(0) = 2
x = 5t + 2