Testing For Convergence
This quick and simple test can only be used to prove a series' divergence
What is the Nth Term Test?
This simple method of integration requires you to add one to the power and divide by the new power
What is Undoing the Power Rule?
The very first method of differentiation that we learned that is used for polynomials
What is the Power Rule?
To use this theorem, a function must be differentiable on the open interval (a,b) and continuous on the closed interval [a,b]
What is MVT?
This renowned mathematician and physicist is often credited with discovering calculus
Who is Sir Issac Newton?
This test can only be used when you know that the series is always decreasing, continuous and positive
What is the Integral Test?
This integration method needs both a function and its derivative inside the integral
What is U-substitution?
This formula is used when differentiating a function divided by another function
What is (f'(x)g(x)-g'(x)f(x))/(g(x)^2)?
These 3 criteria must be met before concluding a function is continuous
What are F(a) is defined, limit as x->a exists and that the two match each other?
This greek philosopher is known for creating many famous trig identities
Who is Pythagoras?
This test can be used to prove both convergence and divergence as long as the result is positive and finite
What is the Limit Comparison Test?
This useful technique is used to integrate two functions multiplied together
What is Integration by Parts?
This essential formula is used when differentiating a function inside another function
What is F'(G(x))*G'(x)?
A limit must meet this criteria before using l'hopitals rule
What is an Indeterminate Form?
This mathematician created the famous constant in mathematics, e
Who is Leonhard Euler?
This beloved test is especially handy when trying to find an interval of convergence
What is the Ratio Test?
This method of integration results in the sum of two natural logs
What is Partial Fraction Differentiation?
When doing this kind of differentiation, don't forget to multiply by dy/dx whenever differentiating y
What is Implicit Differentiation?
One of these two formulas are often found in derivatives in disguise
What is the limit as x->0 of (F(x+h)-F(x))/h or the limit as x->a of (F(x)-F(a))/x-a
This mathematician is known for creating widely used notations such as dy/dx
Who is Gottfried Wilhelm Leibniz?
In order to prove Conditional Convergence, these four conditions must be met
What are always decreasing terms, alternating terms, absolute divergence and an Nth term of 0?
When doing this kind of integration, one must remember a factor if 1/2 and an exponent of 2
What is polar Integration?
This formula is used for differentiating an inverse function
What is F'(x)=1/G'(F(x))?
We used this theorem at the very beginning of the year to evaluate the limit as x -> 0 of sinx/x
What is Squeeze Theorem?
This mathematician sold his work to Guillaume de l'Hôpital, who would later publish it as his own
Who is Johann Bernoulli?