Show:
Limits and Continuity
Differentiation
Integration
Differential Equations
Functions
100
This is a y-value to which a function approaches as x approaches c.
What is a limit?
100
This is the derivative of 4x^3 + 2x^2 + 5.
What is 12x^2 + 4x?
100
One is a function whose derivative is the original function, and the other is a number that is the summation of a function between x=a and x=b.
What is the difference between a definite and an indefinite integral?
100
This is the solution of a differential equation when no initial condition is given.
What is a General Solution?
100
When each value of x determines exactly one value of y, it is called this.
What is a function?
200
These are limits in which x approaches c from either a higher or lower value.
What are one-sided limits?
200
This is the derivative of (13x^2-5x+8)^(1/2)
What is (26x-5)/(2(13x^2-5x+8)^(1/2))?
200
This is the integral of x^3 + 7x^2 + x + 3
What is (x^4)/4 + (7/3)(x^3) + (x^2)/2 + 3x + C?
200
This is the first step of solving a differential equation.
What is the separation of variables?
200
This is the amplitude of the function, y=3sin(4x+2)
What is 3?
300
This is what results when x approaches a c-value that would make the limit undefined.
What is an infinity situation?
300
When this limit exists, f(x) has a slope at x=x0.
What is the limit of (f(x0+h)-f(x0))/h as h approaches 0?
300
This is the integral of csc(u)du.
What is ln(abs(csc(u)-cot(u))) + C?
300
This is an additional step when solving for y in a differential equation that is necessary in certain situations.
What is "checking the initial condition"?
300
This is the formula for the lower half of a circle.
What is -((r^2)-(x^2))^(1/2)?
400
This value of k makes the following piecewise function continuous everywhere: f(x)=kx^2 when x < or = 2, f(x)=2x+k when x > 2.
What is 4/3?
400
These are at least 3 of the 4 techniques of differentiation.
What are the derivative of a constant equals zero, the power rule, the constant multiple rule, and the sum and difference rule? (Any 3)
400
This is the integral of (x^2)/(x^2+1)dx.
What is x - tan^(-1)(x) + C?
400
This is the answer to the differential equation, dy/dx = (y^2)(e^x).
What is y = -1/((e^x)+C)?
400
-π/3 is the answer to this inverse sine function.
What is sin^(-1)(-(3^(1/2))/2)?
500
This is the limit of the function (5-x^(1/2))/(x-25) as x approaches 25.
What is -1/10?
500
This is the derivative of the function, (5-cos(x))/(5+sin(x)).
What is (5sin(x)-5cos(x)+1)/(5+sin(x))^2?
500
This is the integral of (e^x)/((1-e^2x)^(1/2))dx.
What is sin^(-1)(e^x) + C?
500
This is the answer to the differential equation, dy/dx = e^(x-y).
What is y=ln(e^x+C)?
500
This is the value of x when log(x^(3/2)) - log(x^(1/2))=5.
What is 10^(5)?