So this week in calculus, we spent most of the week preparing for our tests on Wednesday and Thursday, and on Friday we reviewed limits.
Lim as x ->-10 x+10/ x^2 – 100
If you plug in 10 into the bottom you get zero so you have to rely on other methods.
In this case, the bottom can factor out to (x-10)(x+10), cancelling out the (x+10)s and leaving you with 1/ (x-10).
You now can plug in your -10 and get -1/20 as your limit.
Example 2: Find the limit:
Lim x-> 0 sin^5x/x^5
Since you cannot factor anything out, you have to plug into the table function of your calculator.
Hit y= and plug in your equation, don’t forget to put parentheses then hit 2nd graph.
Once in your table function, you have to enter numbers to the right of zero and to the left of zero.
0-.1= .9917
0-.01= .99992
0-.001=1
0+. 001=1
0+. 01= .99992
0+. 1= .9917
The limit as x approaches 0 is 1.
To find the limit as x approaches infinity, you use your limit rules, which are:
1. If the degree at the top is greater than the degree at the bottom than the limit is + or – infinity.
Lim x-> infinity 4x^2+3/ 5x+9
Limit= infinity
2. If the degree at the top is less than the degree at the bottom, then the limit is zero.
Limit = 0
3. If the degree at the top is equal to the degree at the bottom, then you divide the coefficients to find your limit.
Lim x-> infinity 3x^2+8/ x^2+ 7
Lim= 3
I seem to still be having trouble with graphs such as when giving the graph of f’(x) and you have to find where f’’(x) is concave up or down or where f(x) is increasing or decreasing. I understand what words go with each graph except I don’t understand how to find what they are asking for. Also, if the question asks to find where f(x) is concave up or down, do you find where f’’(x) is concave up or down because concave up and down goes with the second derivative? Or do you find where the original graph is concave up or down?
Help would greatly be appreciated since this shows up on every test.
Ok, so suppose you're looking at a graph of f'(x) and the question is asking you where the tangent lines are on the graph of f(x).
ReplyDeleteSay on the graph f'(x) there are zeros at -4, -2, 0, 2, and 4.
When you're looking at derivative of a graph and asked to find things on it's origional function, you switch places. Maximums and minimums on a graph a derivitave will be zeros on the graph of the origional function. Just the same, zeros on a graph of a derivitave will be maximums and minimums on its origional function graph.
Also, if a f'(x) graph is given and it asks whether the f(x) graph starts concave up or down, you look at the f'(x) graph and see if the slope is increasing or decreasing. If the slope starts off increasing, then your f(x) graph will start off concave up. If the slope is decreasing, your f(x) graph will start concave down.
I hope this helps