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When you see… Find the zeros You think…

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To find the zeros...

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When you see… Find equation of the line tangent to f(x) at (a, b) You think…

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Equation of the tangent line

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You think… When you see… Find equation of the line normal to f(x) at (a, b)

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Equation of the normal line

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You think… When you see… Show that f(x) is even

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Even function

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You think… When you see… Show that f(x) is odd

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Odd function

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You think… When you see… Find the interval where f(x) is increasing

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f(x) increasing

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You think… When you see… Find the interval where the slope of f (x) is increasing

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Slope of f (x) is increasing

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You think… When you see… Find the minimum value of a function

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Minimum value of a function

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You think… When you see… Find critical numbers

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You think… When you see… Find inflection points

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You think… When you see… Show that exists

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Show exists Show that

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You think… When you see… Show that f(x) is continuous

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. f(x) is continuous

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You think… When you see… Find vertical asymptotes of f(x)

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Find vertical asymptotes of f(x) Factor/cancel f(x), if possible Set denominator = 0

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You think… When you see… Find horizontal asymptotes of f(x)

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You think… When you see… Find the average rate of change of f(x) at [a, b]

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Find the average value of the derivative of f(x) : Average rate of change of f(x)

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You think… When you see… Find the instantaneous rate of change of f(x) At x=a

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Instantaneous rate of change of f(x) Find

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You think… When you see…

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Average value of the function

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You think… When you see… Find the absolute maximum of f(x) on [a, b]

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Find the absolute minimum of f(x)

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You think… When you see… Show that a piecewise function is differentiable at the point a where the function rule splits

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Show a piecewise function is differentiable at x=a

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You think… When you see… Given s(t) (position function), find v(t)

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Given position s(t), find v(t)

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You think… When you see… Given v(t), find how far a particle travels (total distance traveled)on [a, b]

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Given v(t), find how far a particle travels on [a,b]

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You think… When you see… Find the average velocity of a particle on [ a, b ]

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Find the average rate of change on [a,b]

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You think… When you see… Given v(t), determine if a particle is speeding up at t = a

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Given v(t), determine if the particle is speeding up at t=a

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You think… When you see… Given v(t) and s(0), find s(t)

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Given v(t) and s(0), find s(t)

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You think… When you see… Show that the Mean Value Theorem holds on [a, b]

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Show that the MVT holds on [a,b]

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You think… When you see… Find the domain of f(x)

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Find the domain of f(x)

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You think… When you see… Find the range of f(x) on [a, b]

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Find the range of f(x) on [a,b]

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You think… When you see… Find the range of f(x) on

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Find the range of f(x) on

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You think… When you see… Find f ’(x) by definition

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Find f ‘( x) by definition

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You think… When you see… Rate of change of y is increasing proportionally to y

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y is increasing proportionally to y. y is increasing proportionally to y

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You think… When you see… Find the line x = c that divides the area under f(x) on [ a, b ] into two equal areas

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Find the x=c so the area under f(x) is divided equally

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You think… When you see…

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Fundamental Theorem

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You think… When you see…

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Fundamental Theorem, again

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You think… When you see… The rate of change of population is …

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Rate of change of a population

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You think… When you see… The line y = mx + b is tangent to f(x) at (a, b)

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y = mx+b is tangent to f(x) at (a,b). y = mx+b is tangent to f(x) at (a,b)

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You think… When you see… Find area using left Riemann sums

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Area using left Riemann sums

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You think… When you see… Find area using right Riemann sums

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Area using right Riemann sums

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You think… When you see… Find area using midpoint rectangles

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Area using midpoint rectangles

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You think… When you see… Find area using trapezoids

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Area using trapezoids

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You think… When you see… Solve the differential equation …

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Solve the differential equation...

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You think… When you see… Meaning of

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Meaning of the integral of f(t) from a to x

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You think… When you see… Given a base, cross sections perpendicular to the x-axis that are squares

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Semi-circular cross sections perpendicular to the x-axis

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You think… When you see… Find where the tangent line to f(x) is horizontal

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Horizontal tangent line

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You think… When you see… Find where the tangent line to f(x) is vertical

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Vertical tangent line to f(x)

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You think… When you see… Find the minimum acceleration given v(t)

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Given v(t), find minimum acceleration

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You think… When you see… Approximate the value f(0.1) of by using the tangent line to f at x = 0

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Approximate f(0.1) using tangent line to f(x) at x = 0

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You think… When you see… Given the value of F(a) and the fact that the anti-derivative of f is F, find F(b)

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Given F(a) and the that the anti-derivative of f is F, find F(b)

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You think… When you see… Find the derivative of f(g(x))

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Find the derivative of f(g(x))

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You think… When you see… Given, find

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Given area under a curve and vertical shift, find the new area under the curve

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You think… When you see… Given a graph of find where f(x) is increasing

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Given a graph of f ‘(x), find where f(x) is increasing

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You think… When you see… Given a chart of x and f(x) on selected values between a and b, estimate where c is between a and b.

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You think… When you see… Given, draw a slope field

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Draw a slope field of dy/dx

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You think… When you see… Find the area between curves f(x) and g(x) on [a,b]

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Area between f(x) and g(x) on [a,b]

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You think… When you see… Find the volume if the area between the curves f(x) and g(x) is rotated about the x -axis

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Volume generated by rotating area between f(x) and g(x) about the x-axis

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You think… When you see… Find the minimum slope of a function

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Minimum slope of a function

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You think… When you see… Find the derivative of the inverse of f(x) at x = a

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Derivative of the inverse of f(x) at x=a

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You think… When you see… Given v(t) and s(0), find the greatest distance from the origin of a particle on [ a, b ]

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When you see… Given a water tank with g gallons initially being filled at the rate of F(t) gallons/min and emptied at the rate of E(t) gallons/min on, find

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You think… a)the amount of water in the tank at m minutes

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Amount of water in the tank at t minutes

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You think… b) the rate the water amount is changing at m

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Rate the amount of water is changing at t = m

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You think… c) the time when the water is at a minimum

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The time when the water is at a minimum

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When you see… Find a 3 rd degree Taylor polynomial centered at a for f(x) You think…

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3 rd degree Taylor polynomial...

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When you see… You think…

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Derivative of arcsin:

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You think… When you see… Find the radius of convergence of a power series centered at x=a

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Radius of convergence:

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You think… When you see… Find the interval of convergence of a power series centered at a.

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Interval of convergence:

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You think… When you see… Find the error bound of an alternating, decreasing series.

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Error bound

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You think… When you see… Use the Lagrange form of the remainder of a Taylor polynomial centered at x=a.

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Lagrange form of the remainder:

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You think… When you see… Find the velocity and acceleration vector of a particle at t=3 when given x(t) and y(t)

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Velocity and Acceleration Vector

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You think… When you see… Find the speed of a particle in motion on a plane.

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Speed

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You think… When you see… Find the total distance of a particle moving in a plane on the interval (t 1, t 2 ).

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Total Distance Traveled

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You think… When you see… Find the area of a polar graph between

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Area of a Polar Graph

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