Fava
Mrs. Fava's favorite color
What is vibrant Auburn orange?
Find the derivative.
f(x) = 2x2 + 3
What is f'(x) = 4x?
Given the equation x + 4y = 3.
Given that dx/dt = 1, find dy/dt when x=2.
dy/dt = - 1/4
Determine the points where f(x) us discontinuous and categorize the discontinuity as RD, JD or ID.
f(x) = x - 3 / (x2 -9)
x = -3 (Infinite Discontinuity)
x = 3 (Removable Discontinuity)
Evaluate the integral.
∫ (x-2/3 + 1/3x2 - 4x) dx
What is ( 3x1/3 + 1/9x3 - 2x2 + C) ?
Mrs. Fava's alma maters
What are Auburn, Salisbury, George Mason, and NOVA CC?
Find the derivative.
f(x) = 2/3x3 + 1/5x2 + x
What is f'(x) = 2x2 + 2/5x + 1?
A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 2 ft/sec. How rapidly is the area enclosed by the ripple increasing at the end of 12 sec?
Hint: A = πr2
dA/dt = 96 ft2/sec
Solve using separation of variables.
dy/dx = 2(1 + y2)x
y = tan(x2 + C)
Evaluate the integral.
∫ (-sin x - csc x cot x) dx
What is (cos x + csc x + C) ?
Mrs. Fava's favorite table group
What is Table#3?
Find f'(2).
f(x) = (x+2)2
What is f'(2) = 8?
A spherical balloon is inflated so that the volume is increasing at a constant rate of 4 ft3/min. How fast is the diameter of the balloon increasing when the radius is 2 ft?
Hint: V = (4/3)πr3
dd/dt = 1/2π ft/min
Divide the interval into n = 3 subintervals of equal length then compute the right endpoint of each subinterval.
f(x) = x3; [-2, 4]
R3 = 144
Evaluate the integral.
∫(cot2Θ) dΘ
What is (- cotΘ - Θ + C) ?
Mrs. Fava's birthday
What is February 19th?
Find f''(x).
f(x) = sec(x)
What is f''(x) = tan2xsecx + sec3x or
f''(x) = secx (tan2x + sec2x) ?
A 17 ft ladder is leaning against a wall. If the bottom of the ladder is pulled along the ground away from the wall at a constant rate of 4 ft/sec, how fast will the top of the ladder be moving down the wall when it is 8 ft above the ground?
Hint: x2 + y2 = z2
dy/dt = 15/2 ft/sec
Divide f(x) by g(x) using long division.
f(x) = x4 - 8x2 + 11x + 1
g(x) = x + 2
x3 - 2x2 - 4x + 19 - 37/(x+2)
A particle moves along a line so that at any time t > 0 its velocity is given by v(t) = (1 + sin t). Use the information to find the position function of the particle.
s(0) = -3
What is s(t) = t - cos t - 2
Mrs. Fava's maiden name
What is Zimmerman?
A particle moves along a line so that at any time t > 0 its position is given by x(t) = t + 2sin(t). Find the values of t for which the particle is at rest.
What is t = 2π/3 , 4π/3?
Car A is traveling west at 50 mi/hr and Car B is traveling north at 60 mi/hr. Both are headed for the intersection of the two roads. At which rate are the cars approaching each other when Car A is 0.3 mi and Car B is 0.4 mi from the intersection.
Hint: A2 + B2 = C2
dC/dt = 78 mi/hr
Find the limit.
limx->∞ lnx/x
limx->∞ = 0
A particle moves along a line so that at any time t > 0 its acceleration is given by a(t) = (1/t2). Use the information to find the position function of the particle.
s(1)=2
v(1)=0
What is s(t)= - ln |t| + t - 1 ?