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Derivatives
Particle Motion
Limits
Definitions
MISC
100
The first derivative of f(x)= x^2-16x-28
What is f'(x)= 2x-16
100
The position of a particle (in inches) moving along the x-axis after t seconds have elapsed is given by the following equation. s=f(t)=t^4-2t^3-6t^2+9t. Calculate the velocity of the particle at time t.
What is v(t)= 4t^3-6t^2-12t+9.
100
Lim (x-2x^3+1)/(4x^3-4x^2+3) X-> infinity
What is -1/2
100
The definition of the intermediate value theorem.
What is a continuous function, f, with an interval, [a,b], as its domain, takes values f(a) and f(b) at each end of the interval, then it also takes any value between f(a) and f(b) at some point within the interval.
100
State the formula of the power rule for derivatives.
What is f(x)g'(x)+f'(x)g(x)
200
The first derivative of f(x)= (x^2-5x-7)/(2x-6)
What is f'(x)= (2x^2-12x+44)/(2x-6)^2 OR f'(x)= (2(X^2-6x+22))/(2x-6)^2
200
If the position of a particle is given by x(t)= 100-16t^2, find the position of the particle when the velocity is zero.
What is x= 100.
200
Lim f((3x+h)-f(3x))/(h) h-> 0
What is 3
200
State the mean value theorem.
What is if f(x) is continuous on the interval [a,b] and differentiable on the interval (a,b) then there is at least one number c in the interval (a,b) that is a
200
Find any points where the graph fails to be differentiable and explain why.
What is y is not differentiable at x=-7/5. Because of a vertical tangent.
300
The first derivative of f(x)= log(4x^2-8x+7)
What is f'(x)= (8x-8)/(4x^2-8x+7)
300
s(t)= 3t^2+5t+2 describes a particles motion with units in meters. Find the instantaneous velocity and acceleration at t= 4 seconds.
What is v(4)= 29m/s a(4)= 6 m/s^2
300
Lim (x^2+1)/(x^5+2) X-> infinity
What is infinity or DNE
300
State the extreme value theorem.
What is a real valued function f is continuous in the closed and bounded interval [a,b] then f must have attain a maximum and a minimum, each at least once.
300
A function fails to be differentiable if it has a...
What is a cusp, vertical tangent or discontinuity corner.
400
The first derivative of f(x)= sin(x)*cos(4x)
What is f'(x)= cos(x)cos(4x)-4sin(x)sin(4x)
400
An object moving on a horizontal line has a velocity v(t)= 5cost mph in the time interval 0≤t≤2π. Set up a single integral to find the total distance traveled in the time interval 0≤t≤2π. Then use a calculator to evaluate the integral.
What is *Integral sign* (0 to 2π) |5cost| dt= 20 miles.
400
Lim (2x+3)/(3x^2+x) X-> infinity Where is the horizontal asymptote if any.
What is y= 0
400
State the definition of continuity.
What is a function f(x) is continuous on a set if it is continuous at every point of the set.
400
Integrate the following. *Integral sign* (7x+9)^1/2 dx
What is (2/21)(7x+9)^3/2 + C
500
The first derivative of f(x)= (x+4)/(2x-5)
What is f'(x)= (-13)/(2x-5)^2
500
When a particle is moving along the x-axis, and the velocity is negative. The particle is doing what? (Hint: Think about direction.)
What is moving to the left.
500
Is this function continuous f(x)= 2/x. Explain if yes/no.
What is no since f(0)= infinity. Lim f(x)= -infinity does not equal Lim f(x)= infinity. X-> 0^+. X-> 0^-
500
State what a limit is.
What is let f(x) be a function defined on an open interval D that contains C, except possibly at x=c. Let L be a number. Lim f(x)= L. X->
500
Find dy/dx and d^2/d^2x of the following equation. y=3x^4-4x^3/2
What is y'= 12x^3-6x^1/2 And y"= 48x^2-3x^-1/2