Limits
The limit exists at x=c if
What is the lim x->c- f(x) = lim x->c+ f(x)?
A 30ft ladder is propped up against a wall. When the ladder is 3ft away from the base of the wall, it is sliding at 2ft/min down the wall. What is the rate at which the ladder slides across the floor
What is 19.900 ft/min?
The anti-derivative of f'(x)=un
What is f(x)=un+1/(n+1)?
The first step in solving a dy/dx differentiation problem
What is separating the variables onto opposite sides of the equation?
The intermediate value theorem.
What is if f(x) is continuous on [a,b] and f(c) is between f(a) and f(b) then c is on [a,b]?
The function is continuous at x=c if
What is lim x->c- f(x) = lim x->c+ f(x) = f(c)?
A 45ft ladder is propped up against a wall. When the ladder is 35ft from the ground, it is sliding at a rate of 4ft/min across the floor. What is the rate the ladder slides down the wall
What is a rate of 3.232 ft/min down the wall?
The anti-derivative of f'(x)=x2
What is f(x)=x3/3?
Solve for y with the initial condition y(pi)=1 for dy/dx=2sinx
What is y=-2cosx-1?
The extreme value theorem.
What is if the function is continuous on a closed interval then f has both a minimum and maximum value on the interval?
L'Hospital's rule
What is when the limit of a numerator and denominator of a function both equal zero, so you take the derivative of both of them separately and solve for the limit?
A balloon is being filled with air at a rate of 8ft3/min. When the radius is 4ft, at what rate is the radius of the balloon increasing.
What is 0.040 ft/min?
The anti-derivative of f'(x)=2x8/3
What is f(x)=2x9/27?
Solve for y if y=1 when x=0 for dy/dx=ycosx
What y=esinx?
The mean value theorem.
What is if the function is continuos on [a,b] and differentiable on (a,b), there is at least one point where f'(x)=(f(b)-f(a))/(b-a)?
The lim x->infinity of (5x+6x2)/(3x-8)
What is infinity?
Water is poured into a cylindrical canteen with a height of 4ft and radius of 2ft. The height of the water level is increasing by 4ft/min. At what rate is the volume increasing.
What is 150.796 ft3/min?
The anti-derivative of f'(x)=cos2(3x)
What is f(x)=sin3(3x)/9?
Solve for dx/dt if dy/dt=-2 at the point (1,3) for the function 2x2+2xy=14
What is 2/5?
The Rolle's theorem.
What is if the function is continuous and differentiable and f(a)=f(b) then there is at least one point where f'(x)=0?
The lim x->0 of sin(x)/x; lim x->infinite of sin(x)/x
What is 1; 0?
A kite 40 ft above the ground moves horizontally at a rate of 3 ft/sec. At what rate is the angle between the string and the horizontal decreasing when 80 ft of string has been let out.
What is -0.019 rad/sec?
The anti-derivative of f'(x)=(cscxcotx)3
What is f(x)=(-cscx)4/4?
Find d2y/dx2 for the curve x2+y2=27-xy at the point (3,-6). Does the curve have a local maximum or minimum or neither at this point.
What is 2/9 and a local minimum?
The theorem and solution to f(x)=x2+4x-6 [1,5]
What is by the MVT, x=3?