So these holidays went by way too fast. I am NOT ready to come back to school but ummmmm here’s my blog.
Limit rules since I always miss those.
When the limit is approaching infinity:
Top degree is less than the bottom degree = 0
Top degree is greater than the bottom degree = infinity
Top degree is equal to the bottom degree = top coefficient over the bottom coefficient
For example:
Lim 4x – 2/ x^2 = 0
x>infinity
Lim 3x^4 – 2x + 5/ 6x = infinity
x>infinity
Lim 2x^2 – 1/ 3x^2 = 2/3
x>infinity
When the limit is approaching a number:
Three steps-
1. Factor out the top and the bottom
2. Look for cancellations
3. Plug in the number
Riemann Sums
Ever since that worksheet we did in class this is a LOT easier.
Delta x = b – a /# of subintervals
LRAM- left hand approximation –obviously finds the area on the left side of the curve : deltax[f(a)+f(a+deltax)+...f(b)]
RRAM- right hand approximation – finds the area on the right side of the curve: deltax[f(a+deltax)+...f(b)]
MRAM- middle approximation – finds the area on top of the curve: deltax[f(mid)+f(mid)+...]
Trapezoidal- most accurate, uses trapezoids instead of rectangles: deltax/2[f(a)+2f(a+deltax)+2f(a+2deltax)+...f(b)]
Hmmm stuff I need help with?
Related rates (and I already know the steps so please don’t post those), linearization (knew how last week but forgot again), normal/tangent lines, and problems like the ones with a ladder leaned up on a house or whatever..
Obviously I can use help on a lot of things so feel free to be nice (:
Sooo back to school tomorrow, can’t wait.
SIKEEEEEEE, kbye.
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Tangent line
ReplyDeleteYou need a point and a slope. You are usually given x. Plug in x to find your y. Take derivative and plug in x to find your slope. Plug into point-slope formula y-y1=m (x-x1)
Example: Find the equation of the tangent line to 9x^2 +16y^2 = 52 through (2, -1)
Since you have a point, all you have to do is find the slope.
Derivative: 18x + 32 y dy/dx = 0
dy/dx = -18x / 32y
Now plug in the point: -18 (2) / 32 (-1)
36/32 = 9/8
Plug into point slope: y+1 = 9/8 (x-2)
It may be written in a different form.
Normal line is the same steps except you use the negative reciprocal of your slope. In this case slope would equal -8/9 and the equation of the normal line would be
y+1 = -8/9 (x - 2)
You first need a point and a slope. You are usually given x. Plug in x to find your y. Take derivative and plug in x to find your slope. Plug into point-slope formula y-y1=m (x-x1)
ReplyDeleteRelated Rates FTW!!!
ReplyDeletex and y are both differentiable functions of t and are related by the equation y=2x^3-x+4. When x=2 dx/dt=-1 Find dy/dt.
Some people are freaking out in their heads by now but not to fear, related rates problems are similar to optimization and implicit derivatives.
Steps for Related Rates Problems:
1. Identify all variables and equations.
2. Make a sketch and label. *VERY IMPORTANT*
3. Write an equation that involves your variables. *You can only have one unknown so a secondary equation may be given* (Usually this step is needed for word problems that ask you to find the rate at which a side of a triangle moves or the volume of a sphere changes.)
4. Take the derivative with respect to time, which is t.
5. Plug in all variables and solve.
Sure there are a lot of steps involved but they flow from one to the next so simply its like there is only 1 step: solve.
Step 1. Identify all variable and equations.
y=2x^3-x+4 x=2 dx/dt=-1 and dy/dt=?
Step 2. Make a sketch and label.
Um...since I am doing this on a blog I will not sketch and label the problem.
Step 3. Write an equation involving all variables.
Already given to us (y=2x^3-x+4)
Step 4. Differentiate with respect to "t".
dy/dt=6x^2(dx/dt)-1(dx/dt)
Step 5. Plug in a solve.
dy/dt=6(2^2)(-1)-1(-1)
dy/dt=-23