Integrals
This is something included in answers for indefinite integrals but not definite integrals.
What is +C?
A series can be described as this operation over a sequence.
What is the sum?
This is a common method used when solving differential equations that involves moving all x's to one side of the equation.
What is separation of variables?
This is the degree that your TA (Kristin) is currently finishing.
What is a Master's in Pure Mathematics?
When finding the area of a region bounded by a larger function A and a smaller function B (so A is above B on the graph), this is the equation used inside the integral.
What is A-B?
This would be a good u value to pick for the integral of [sin^10(x)cos(x)].
What is u=sin(x)?
In a geometric series, the series converges only if this condition is met.
What is abs(r)<1?
This is the general subtraction setup used to find the equation of the rate of change of mass of a substance in a tank filling and draining with water.
What is flow in - flow out?
Your written work for the final exam needs to be emailed to Keshav by this time frame.
What is 10 minutes?
When finding the volume of a cylinder with an integral using disks, you take the integral over this formula followed by a dx or dy.
What is the area of a circle/ slice or (pi)r^2?
This technique is a way to more easily evaluate integrals of large fractions.
What is partial fraction decomposition?
The Divergence Test can be used to potentially show a series does this but cannot show if it does this.
What is diverges and converges?
In an exponential growth model, the concept represents the maximum amount a population can reach given the environment's constraints.
What is carrying capacity?
A Maclaurin Series is a Taylor Series centered at this location.
What is x=0?
When revolving a region about the y-axis and using the disk/washer method, the integral should be in terms of this variable.
What is y?
This formula is used in the beginning steps of trig substitution problems.
What is the Pythagorean theorem/ identity?
When evaluating a series that has factorial terms in a fraction, it is easiest to use this test of convergence.
What is the ratio test?
This is the general formula for the mass of a substance in a tank filling and draining with water. (Final solution to mixing problem)
What is m(t) = Ce^(rt) + b/r
This test is needed in order to find the interval of convergence of a series.
What is the ratio test?
When revolving a region about the y-axis and using the shell method, the integral should be in terms of this variable.
What is x?
After completing most the work of a definite trig sub problem, this is the final step to having the correct answer.
What is putting the answer in terms of x (or whatever the original variable was)?
If a sequence b_n is larger than a sequence a_n and the series of b_n converges, then the series of a_n does this.
What is converges?
You use this piece of information to solve for this term to get a final answer of a differential equation.
What is initial value and C/ constant?
This formula is used to tell us what an infinite geometric series converges to.
What is a/(1-r)?
If you're finding the volume of a cylinder rotated around the y-axis using the shell method, this is the formula you should integrate over.
What is 2(pi)xh?