Understanding concepts?what's the difference between flat and tangent?
829333
Your serious question may be off-tangent to folks in this category, though.
760338
There is an intrinsic difference between the 2 statements. I am a mechanical engineer and know that a surface can seem to be smooth and feel like it is when in fact it isn`t. The word "is" is  positive and the word "seems" is subjective so both sentences are correct.
819742
The first derivative is the slope of the line that is tangent to the graph.  If there is a maximum or minimum, the tangent line at that point will be horizontal, so its slope is 0.  \n\nThe second derivative is 0 when there is an inflection point. An inflection point is a place on the graph where it changes the direction of the concavity. \n\nIn the two cases above, the converse is not necessarily true.  That is, just because the first derivative is 0 doesn't mean there has to be a max/min there.\n\n If the second derivative is positive, the graph is concave upward which means like a regular "U".  If it's negative, it's concave downward like an upside-down "U".
245265
The derivative of sinx is just cosx, but the derivative of cosx is -sinx.  Then the derivative of -sinx is -cosx, and the derivative of that is sinx.  So it actually takes four applications of the derivative to get back where you started rather than two.  \n\nIf you're comfortable with the definition of the a derivative you can work it out and see that that's true.  Otherwise, just draw the graphs and look at where the slopes are negative and where they're positive.\n\nHope that helps!\n\nPS.  When you're looking at the page your question is on, you can click "additional information," and add more there rather than making a new question.  Saves you five points. :-)
667321
A secant is a line that intersects a circle in two points. Therefore only sometimes does it pass through the center of the circle.\n\nA tangent is a line that intersects a circle in exactly one point. Therefore it can never pass through the center of a circle
350288
You question is incomplete....or at least requires more information, as it is, it is too general.\n\nWhat are the conditions are are talking about here?\nAre both balls pushed with some constant force?  As they rolled down an incline?  Are they already in motion?\n\nWhat type of surface are they on?  A smooth (frictionless) surface?  A rough surface where friction needs to be taken into account?  Are both balls solid, hollow, one each?\n\nThey are many many variables which need to be taken into account, you cannot just say "big" and "small" and get an accurate answer.\n\nAnd by "greater distance" do you mean translational displacement, or angular displacement?
122440
no difference....just different terms
1053843
Rotation is something turning on its axis.\nRevolution is something going around something else.
474087
do you mean transcendental or tangential? tangendental is not in the dictionary but may be a recent coining ...\n\ntranscendental means something that transcends and has been used with reference to meditation. maybe the other word you give is meant to be existential transcententalism??\n\ntangential means 'at a tangent to'
577604
The essence of calculus is the derivative. The derivative is the instantaneous rate of change of a function with respect to one of its variables. This is equivalent to finding the slope of the tangent line to the function at a point. Let's use the view of derivatives as tangents to motivate a geometric definition of the derivative
333801
I believe both have the same meaning. One is British-English origin ("oriented" I think), and the other is US-English origin. They tend to be used interchangeably much to my annoyance ;-)
663303
it would be called tangent...if it touches the outside of the circle once.\n\nthe radius of the circle is a line that goes through the cirlce half way, the diamiter is a line that goes through the circle and cuts it right in half, so the radius is half the diamiter.\n\nsecant intersects a cirlce at two points.\n\nSO the answer is tangent.\n\nhope this helps.
201825
Well um...\n\na = r''\n\na = (tangential acceleration * unit tangent) + (normal acceleration * unit normal) = (at * T) + (an * N)\n\nT and N are your unit tangent and unit normal of the function that defines your position.\n\nat = (r' dotted with r'') / (|r'|)\n\nThose are the tangential acceleration components but for this problem i think that you are going to have to reparamiterize your curve.
425296
Instantaneous rate of change of a function (7 words),\n\nOR,\n\nSlope of the tangent line (5 words). :P
899768
Its like instantaneous speed. It is the speed or wateva you are trying to find between two really reallly reallllly close points. Example if you are trying to find the derivitive of 2 then plug in 1.999999 or 2.000001 into the equation, doesn't matter. \n\nOtherwise, it is the slope of the tangent of a point.
666325
Calculus is not an advanced mathematical concept; I was taught it at a bog standard state school starting when I was 12 years old. It is really simple; it starts by being about finding the area under a graph and then (of course) being able to do the calculation in reverse.  Differentiation and Integration. You can investigate the rate of change, and it introduces you to the philosophical notions of tiny differences, infinity and the way that geometry is a graphical form of algebra.\n\nAt it's root, Newton would have seen that (for example) speed equals distance over time.  This is m/s or miles per hour... called a linear equation because you can plot a straight line (m/s) if one axis is "m" and the other is "s".  The angle the line makes, the steepness, introduces trigonometric ratios.  The steeper the incline angle, the faster something is going in a given time.\n\nNewton began devising his calculus based on the notion that all the marvelous interlinked things you can do with linear equations, can be done for curves... but it all depends on thinking of a tiny part of the curve...\n\nThe tiny teeniest bit of a curve is almost a line... or a curve is just a series of tiny straight lines with incline angles...\n\nIn the end it is not "important" to learn calculus, it is not very useful in everyday life.  At best it may be thought of as useful in philosophy merely because it is reversible, and because it involves weird notions about error and approximation for the sakes of utility.\n\nADVANCED mathematics (not calculus!) such as the theory of knots, surface landscapes, three dimensional matrices etc is very close to philosophy; it will sharpen your LOGIC to be more stringent and you will produce tighter proofs and more cohesive theories if you learn the advanced mathematical mindset...\n\nFor example, SIMPLE maths suggests that we know and accept 1+1=2, ADVANCED mathematics asks how and why 1+1=2, and what would happen if 1+1=5 etc.  i.e. different models within which to work.\n\nProbably the simplest and first introduction to all this is when people are told to use numbers with base 8 or base 2 instead of base 10.\n\nBinary or Hexadecimal is quite a philosophical revelation to some people!  Try doing a simply multiplication calculation using Roman numerals. ... challenge the accepted norms and think freely (maths will allow you to do this like nothing else).  Appreciate the beauty of mathematics, theoretical proofs to applied natural philosophy, fractals, and more besides.
382957
I you can express the problems in mathematical relations, yuo can use calculus  everywhere. For businesses you can use differentiation to find sensitivity of for example of profit to  a unit change in cost or sales or production.  you can use integration to find out over all profit or production, etc.