Section 1

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y = cos(x), y' =

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Mar 1, 2020

Cards (67)

Section 1

(50 cards)

y = cos(x), y' =

Front

y' = -sin(x)

Back

Particle is moving to the right/up

Front

velocity is positive

Back

mean value theorem

Front

if f(x) is continuous and differentiable, slope of tangent line equals slope of secant line at least once in the interval (a, b) f '(c) = [f(b) - f(a)]/(b - a)

Back

y = log (base a) x, y' =

Front

y' = 1/(x lna)

Back

rate

Front

derivative

Back

y = e^x, y' =

Front

y' = e^x

Back

When f '(x) is increasing, f(x) is

Front

concave up

Back

If g(x) = ∫ f(t) dt on interval 2 to x, then g'(x) =

Front

g'(x) = f(x)

Back

y = tan⁻¹(x), y' =

Front

y' = 1/(1 + x²)

Back

y = x cos(x), state rule used to find derivative

Front

product rule

Back

Intermediate Value Theorem

Front

If f(1)=-4 and f(6)=9, then there must be a x-value between 1 and 6 where f crosses the x-axis.

Back

Alternate definition of derivative

Front

limit as x approaches a of [f(x)-f(a)]/(x-a)

Back

Fundamental Theorem of Calculus

Front

∫ f(x) dx on interval a to b = F(b) - F(a)

Back

right riemann sum

Front

use rectangles with right-endpoints to evaluate integrals (estimate area)

Back

left riemann sum

Front

use rectangles with left-endpoints to evaluate integral (estimate area)

Back

y = a^x, y' =

Front

y' = a^x ln(a)

Back

y = sin⁻¹(x), y' =

Front

y' = 1/√(1 - x²)

Back

When f '(x) changes from increasing to decreasing or decreasing to increasing, f(x) has a

Front

point of inflection

Back

y = csc(x), y' =

Front

y' = -csc(x)cot(x)

Back

When f '(x) is positive, f(x) is

Front

increasing

Back

To find absolute maximum on closed interval [a, b], you must consider...

Front

critical points and endpoints

Back

trapezoidal rule

Front

use trapezoids to evaluate integrals (estimate area)

Back

y = cot⁻¹(x), y' =

Front

y' = -1/(1 + x²)

Back

If f '(x) = 0 and f"(x) > 0,

Front

f(x) has a relative minimum

Back

Product Rule

Front

uv' + vu'

Back

If f '(x) = 0 and f"(x) < 0,

Front

f(x) has a relative maximum

Back

area under a curve

Front

∫ f(x) dx integrate over interval a to b

Back

average value of f(x)

Front

= 1/(b-a) ∫ f(x) dx on interval a to b

Back

y = sec(x), y' =

Front

y' = sec(x)tan(x)

Back

y = cos²(3x)

Front

chain rule

Back

[(h1 + h2)/2]*base

Front

area of trapezoid

Back

y = sin(x), y' =

Front

y' = cos(x)

Back

y = ln(x), y' =

Front

y' = 1/x

Back

y = tan(x), y' =

Front

y' = sec²(x)

Back

y = cos⁻¹(x), y' =

Front

y' = -1/√(1 - x²)

Back

Formal definition of derivative

Front

limit as h approaches 0 of [f(a+h)-f(a)]/h

Back

y = cot(x), y' =

Front

y' = -csc²(x)

Back

When f '(x) is decreasing, f(x) is

Front

concave down

Back

When is a function not differentiable

Front

corner, cusp, vertical tangent, discontinuity

Back

Average Rate of Change

Front

Slope of secant line between two points, use to estimate instantanous rate of change at a point.

Back

Instantenous Rate of Change

Front

Slope of tangent line at a point, value of derivative at a point

Back

When f '(x) changes fro positive to negative, f(x) has a

Front

relative maximum

Back

Linearization

Front

use tangent line to approximate values of the function

Back

When f '(x) is negative, f(x) is

Front

decreasing

Back

Particle is moving to the left/down

Front

velocity is negative

Back

y = ln(x)/x², state rule used to find derivative

Front

quotient rule

Back

When f '(x) changes from negative to positive, f(x) has a

Front

relative minimum

Back

absolute value of velocity

Front

speed

Back

Quotient Rule

Front

(uv'-vu')/v²

Back

Chain Rule

Front

f '(g(x)) g'(x)

Back

Section 2

(17 cards)

To draw a slope field,

Front

plug (x,y) coordinates into differential equation, draw short segments representing slope at each point

Back

cos(pi/3)

Front

1/2

Back

cos(pi/4)

Front

Back

volume of solid of revolution - washer

Front

π ∫ R² - r² dx over interval a to b, where R = distance from outside curve to axis of revolution, r = distance from inside curve to axis of revolution

Back

cos(pi)

Front

-1

Back

cos(pi/2)

Front

0

Back

sin(pi/6)

Front

1/2

Back

sin(pi/2)

Front

1

Back

sin(pi/4)

Front

Back

given v(t) find total distance travelled

Front

∫ abs[v(t)] over interval a to b

Back

cos(0)

Front

1

Back

sin(pi/3)

Front

Back

sin(0)

Front

0

Back

sin(pi)

Front

0

Back

cos(pi/6)

Front

Back

area between two curves

Front

∫ f(x) - g(x) over interval a to b, where f(x) is top function and g(x) is bottom function

Back

To find particular solution to differential equation, dy/dx = x/y

Front

separate variables, integrate + C, use initial condition to find C, solve for y

Back