Section 1
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Find the domain of f(x)
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Date created
Mar 1, 2020
Cards (54)
Section 1
(50 cards)
Find the domain of f(x)
Check the end behavior.
Find critical values.
f'(x)= 0
Find inflection points
f''(x) = 0
Find f'(x) by definition.
Slope at a point.
Find vertical asymptotes of f(x)
A number over zero.
Find the area using midpoint rectangles
...
Find the area using trapezoids
Left Riemann Sum + Right Riemann Sum DIVIDED BY 2.
Find the average velocity of a particle on [a,b]
Position from a to b and divide by b-a.
y is increasing proportionally to y
...
Find the interval where f(x) is increasing.
f'(x)= +
Find the minimum slope of a function
f'' changes from - to +.
Find the derivative of inverse to f(x) at x=a
Check for implicit differentiation. Switch x and y.
The rate of change of population is
dP/dt=...
Find where the tangent line to f(x) is vertical.
Write f'(x) as a fraction. Set the denominator to zero.
Find the line x=c that divides the area under f(x) on [a,b] to two equal areas.
...
Given position function, find v(t)
derivative.
Find the absolute maximum of f(x) on [a,b]
Critical points. Make sure you look at critical points and end points.
Show that a piecewise function is differentiable at the point a where the function rule splits.
The slope at a is the same on both sides.
Find the range of f(x) on (-infinity, infinity)
...
Find the area using left Riemann Sums
Base multiplied by the first value...
Show that f(x) is odd
f(x)= -f(-x). YES. Thats right. Two negatives.
Find the Zeros
f(x)=0
Find where the tangent line to f(x) is horizontal.
Write f'(x) as a fraction. Set the numerator to zero.
Find the derivative. of f(g(x).
Its a chain rule.
Given a picture of f'(x) find where f(x) is increasing.
Make a sign chart of f'(x) and determine where f'(x) is positive.
Find the minimum acceleration given v(t)
First find the acceleration a(t) = v'(t). Then minimize the acceleration by examining a'(t).
The line y=mx+b is tangent to f(x) at (x1,y1)
The two functions share the same slope and y value at x1.
Show that f(x) is continous
limit as it approaches a is the same from both sides.
Given a base, cross sections perpendicular to the x axis are squares.
The area between curves will be your base.
Given v(t) and s(0), find s(t)
Integrate v(t). Set it to s(0). Solve for c.
Given v(t), determine if a particle is speeding up or slowing down at t=k.
v(t) and a(t) are both positive or negative = Speeding up. v(t) and a(t) are inverse = Slowing down.
Find the interval where the slope of f(x) is increasing.
f''(x) = +
Find the area using right Riemann Sums
Base multiplied by the second value...
Find the equation of the line tangent to f(x) at (a,b)
Get x and y. Get the slope at x. y-y1=m(x-x1)
Solve the differential equation.
Separate, integrate, Add C, initial condition. Plug in C. Solve.
Find the Range of f(x) on [a,b]
...
Given the value of F(a) and the fact that the anti-derivative of f is F, find F(b)1
...
Find the instantaneous rate of change of f(x) at a
derivative of f(x) and plug in a
Find the minimum value of a function
f' changes from - to +
Find the horizontal asymptotes of f(x)
top, bottom, neutral heavy.
Mean Value Theorem requirements
closed interval, continuous, differentiable.
Approximate the value of f(0.1) by using the tangent line to f a x=0.
Find the tangent line. Then plug .1 into this line. Make sure you use an approximate sign.
Show that f(x) is even.
f(x)=f(-x)
Show that Rolle's Theorem holds on [a,b]
MVT when a and b have the same height. It means that there is min or max.
Find the average rate of change of f(x) on [a,b]
Slope from a to b.
Show that limx->a exists.
limit as it approachs a from the left and right are the same.
Meaning of an integral.
It gives you the accumulated area under a function.
Find the average value of f(x) on [a,b]
Integrate from a to b. And then divide by b-a. (The interval.)
Find the equation of the line normal to f(x)
negative reciprocal.
Given v(t), find how far a particle travels on [a,b]
Integral of v(t).
Section 2
(4 cards)