RIDING A (CO)SINE WAVE
The period of the function f(x) = 2sin(3x-1) + 4.
What is 2*pi/3?
The horizontal asymptote a rational function with the degree in the denominator is larger than the numerator.
What is y = 0 (x-axis)?
The limit as x approaches 0 of x/x.
What is 1?
The difference between speed and velocity.
What is direction?
What is average rate of change?
The horizontal shift of the function g(x) = -cos(4x+1) + 2.
What is 1/4 units to the left?
The horizontal asymptote of the function y = (2^(-x)+x^3)/(2x-5x^3).
What is y = -1/5?
Let f(x) = x/x. The "value" f(0).
What is undefined?
The difference between instantaneous velocity and the derivative of a function.
All instantaneous velocities are derivatives but not all derivatives are instantaneous velocities. Instantaneous velocity is the application of the notion of a derivative.
The derivative of an odd function.
What is an even function?
The smallest positive value 'x' that solves 2sin(3x+1) - 1 = -1.
The smallest degree polynomial with zeros at x = -2, x = 5 and a double root at x = 1 and passing through the point (0,10).
What is y = -(x+2)(x-5)(x-1)^2?
The limit as x approaches infinity of f(1/x^2 + 2) is equivalent to what other limit...
What is the limit as x approaches 2 from the right of f(x)?
A function which as a negative instantaneous velocity for t < 0 and positive instantaneous velocity for t > 0.
What is f(t) = t^2?
The derivative a function is always negative. The function itself is always...
What is decreasing?
A function that oscillates with maximum of 12 at t = 3, minimum of -2 and period of 10.
What is 7*cos(pi/5*(t-3)) + 5
A rational function with a hole at x = 5, a vertical asymptote at x = 1 and a horizontal asymptote at y = -2.
What is y = (-2(x-5)x)/((x-5)(x-1))?
The limit as x approaches infinity of f(2-1/x^2) is equivalent to what other limit...
What is the limit as x approaches 2 from the left of f(x)?
A function giving the position of a particle that has the same speed at t = -1 and t = 1 by different velocities.
What is y = t^2?
The derivative of a linear function is always...
What is constant?
The range of inverse sine function.
What is [-pi/2, pi/2]?
A polynomial, p(x), of at least degree 5 and the domain of log(p(x)) is all real numbers.
What is x^6+1?
The limit as h approaches 0 of (f(1.83 + h) - f(1.83))/h is equivalent to...
What is f'(1.83)?
Average velocity times the change in time.
What is the change in position?
The equation of a tangent line of the function f(x) at x = a.
What is y = f'(a)(x-a) + f(a)?