Question

what is the difference between capital delta y/capital delta x and dy/dx?

Answer 1

More or less the same

Answer 2

No its not the same!
The question is a little vague, ( could just be me, Im a little vague when I read )
Usually \[\Delta Y \] means the change in y, say \[y_{1} - y_{0}\] where as dy/dx is the derivative, or more importantly its the limit as delta x approaches 0 \[\lim\frac{\Delta y }{\Delta x}\] without the limit \[\Delta y /\Delta x\]
is just the average rate of change

Answer 3

thats great thanks! the notation is the part that usually stumps me rather than the arithmetic!

Answer 4

if we have two points (x1,y1) & (x2,y2) on the curve y=f(x) then, \[\Delta y /\Delta x =(y_2-y_1)/(x_2-x_1)\rightarrow\] is the slope of the line segment joining the two points in the xy-plane, while dy/dx represents the slope of the tangent line to the curve where (x2,y2) becomes very close to (x1,y1). so in general, both slopes are differ from each other with error \[\epsilon\] such that: \[\Delta y / \Delta x-dy/dx = \epsilon\] for the particular case if f(x) is a line not parallel to y-axis then, \[\epsilon=0\] and \[\Delta y / \Delta x = dy/dx = Constant\]