Limits
Limit as x goes to 0 of xlnx (20s)
What is 0
Integral of csc2x dx(30s)
What is -cot(x)+c ?
derivative of tanx(15s)
Sec^2xdx
Write out the Maclaurin series for sinx(30s)
What is x-x^3/3!+x^5/5!-x^7/7!+...
Nationality of Marquis de l'Hôpital(20s)
France
Limit as x goes to 5 of x squared minus 25 over x squared plus x minus 30 (50s)
what is 10/11?
When the graph on a given interval is concave down, a trapezoidal approximation will be...
What is an under-approximation?
The second derivative of f(x)=secx (60s)
What is sec3x+tan2xsecx
This series, whose terms are the reciprocals of the positive integers, is famous for diverging despite the terms getting smaller.(25s)
What is the Harmonic Series?
Name 3 counties in Ireland(25s)
What is Antrim, Armagh, Cavan, Clare, Cork, Derry, Donegal, Down, Dublin, Fermanagh, Galway, Kerry, Kildare, Kilkenny, Laois, Leitrim, Limerick, Longford, Louth, Mayo, Meath, Monaghan, Offaly, Roscommon, Sligo, Tipperary, Tyrone, Waterford, Westmeath, Wexford, and Wicklow?
Limit as x goes to 0 of (sinx-x)/tanx= (60s)
What is 0
Integral of 1/(1+x^2)dx(45s)
What is arctan(x)+c
This theorem guarantees that a continuous, differentiable function with equal values at the endpoints of an interval has at least one interior point where the derivative is zero.
Rolle's Theorem
What is the sum of all odd integers from 50 to 150?(60s)
5000
The formula HCl is used for this chemical compound(25s)
What is Hydrochloric Acid?
This theorem says if a function is bounded between two other functions that converge to the same limit at a point, then the function in the middle also converges to that same limit. (60s)
What is the Squeeze Theorem?
This technique, often used when integrating rational functions, involves decomposing the integrand into simpler fractions, typically requiring the solving of a system of equations to find the coefficients.(45s)
What is Partial Fraction Decomposition?
Name the three places at which a continuous function can be non-differentiable (35s)
Cusp, Corner, Vertical Tangent
Find the common ratio of a Geometric Series whose sum of infinite terms is 8 and its second term is 2.(65s)
1/2
Name 3 countries that starts with the letter F(30s)
What is Fiji, France, and Finland?
The formal definition of a limit involves these two Greek letters
What are epsilon and delta
True or False: The integral of sin2x on the interval for 0 to π is equal to the integral of cos2x on the interval for 0 to π
What is True
If the volume of a sphere with radius 5 m is increasing at a rate of 2 m/s, what is rate at which its radius is increasing?(60s)
1/50π
This type of series is often characterized by consecutive terms that cancel out, leaving only a few terms behind when summed.(30s)
What is a telescopic series?
The year St.Joes opened as a school(30s last question)
What is 1961?