hellllooo claculus.
so to start off on a good note, i atleast get half of the stuff we did this week =)
first of all, i spent all of last year failing at life on our advanced math
tests because i couldn't grasp the concepts of logs if my life depended
on it, but it's a new year babyyy. when i first looked at our work sheet
i wanted to qluit life, but then it all clicked and i was super excited,
which i still am if you can't tell. though i am a little aggravated that
i spent so much time sucking at such simple concepts.
Now when i see someting like
evaluate the expression log279
i actually know what to do with it and not just put a ridiculous answer.
also, the equation of a tangent line, thankfully,
was extremely easy for me. i understood from the first example
Recall :
• A Tangent Line is a line which locally touches
a curve at one and only one point.
• The slope-intercept formula for a line is y = mx + b,
where m is the slope of the line and b is the y-intercept.
• The point-slope formula for a line is y – y1 = m (x – x1).
This formula uses a point on the line, denoted by (x1, y1),
and the slope of the line, denoted by m, to
calculate the slope-intercept formula for the line.
• The first derivative is an equation for the slope of a tangent
line to a curve at an indicated point.
The equation for the slope of the tangent line to
f(x) = x2 is f '(x), the derivative of f(x).
f(x) = x2
f '(x) = 2x (1)
Therefore, at x = 2, the slope of the tangent line is f '(2).
f '(2) = 2(2)
= 4
Now , you know the slope of the tangent line, which is 4.
All that you need now is a point on the tangent line to be
able to formulate the equation. To find that point, simply plug
the coordinate of the shared point into the original equation, this gives you (2,4)
The only step left is to use the point (2, 4) and slope, 4,
in the point-slope formula for a line. Therefore: Y-4=4(x-2)
NOW FOR WHAT I DON'T UNDERSTAND.
.. they whole arc trig formulas really throw me off and i keep getting
confused on what exactly i do first, or what part of the problem i need
to simplify first, but since b-rob posted that response earlier i
think i understand a little bit better, i just need to stay motivated
and make myself work more problems becuase i know that is
the only way i'm fully going to understand and remember all this.
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the thing that helps me first is to work from the outside in. Solve the first thing you see first. If there's a number before the trig function, bring it out front...then forget about it for the moment. Solve your arctrig part by the formula, then find the derivative of the inside of it. Now you can focus on simplifying and that kind of nonsense.
ReplyDeletefor the arc trig formulas::
ReplyDeletefrom my understanding it's just like everything else just another formula. like for the derivitive of tan(u) it would be sec [squared] (u) multiplied by "u" prime. However, when you have ARC SIN it's:
1
----- all multiplied by "u" prime
1+(u)...the u is squared
now..the simple ones with just a number i can do...as for EVERYTHING else...like the simplifying and stuff...it's tough once you get to the long and crazy ones that deal with different kinds of derivatives within the arc formulas all within the square root or something..
The arc trig problems are actually pretty easy if you know the derivative formulas. All you have to do is plug in and then simplify. Also, it helps if you use the "order of operations" that mrs. robinson told us in order to do the different functions at once. Look at the problem first and find what the first thing you notice about the problem, if there is the quotient rule that's completely obvious that's probably what you do first.
ReplyDeleteYeah, just make sure you work from the outside in and when you finish with an outside part, you cross it out so you know you don't have to do that over again. That's what I do and it helps a lot. It also helps if you do as many problems as you can. You can't figure out what you need help in the most if you don't do the problems.
ReplyDelete