Instructions:

• Answer 50 questions in 15 minutes.
• If you are not ready to take this test, you can study here.
• Match each statement with the correct term.
• Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.

1. Given v(t) find displacement
concave up
? v(t) over interval a to b
general term = 1/n^p - converges if p > 1
? abs[v(t)] over interval a to b


2. y = e^x - y' = y' =
f(x) has a relative minimum
Alternating series converges and general term diverges with another test
e^x
uv' + vu'


3. mean value theorem

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4. If f '(x) = 0 and f'(x) > 0 -...
(uv'-vu')/v²
Slope of tangent line at a point - value of derivative at a point
f(x) has a relative minimum
1/(b-a) ? f(x) dx on interval a to b


5. When f '(x) changes from increasing to decreasing or decreasing to increasing - f(x) has a...
0/0 - 8/8 - 8*0 - 8 - 8 - 1^8 - 0° - 8°
point of inflection
logistic growth equation
concave down


6. y = sin?¹(x) - y' =

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7. Intermediate Value Theorem
p ? r² dx over interval a to b - where r = distance from curve to axis of revolution
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.
Limit as h approaches 0 of [f(a+h)-f(a)]/h
? v (dx/dt)² + (dy/dt)² over interval from a to b


8. Area inside one polar curve and outside another polar curve
concave up
1/2 ? R² - r² over interval from a to b - find a & b by setting equations equal - solve for theta.
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.
a^x ln(a)


9. If f '(x) = 0 and f'(x) < 0 -...
corner - cusp - vertical tangent - discontinuity
Alternating series converges and general term converges with another test
0/0 - 8/8 - 8*0 - 8 - 8 - 1^8 - 0° - 8°
f(x) has a relative maximum


10. slope of horizontal line
zero
uv - ? v du
? A(x) dx over interval a to b - where A(x) is the area of the given cross-section in terms of x
y' = 1/(x lna)


11. Given velocity vectors dx/dt and dy/dt - find speed
f '(g(x)) g'(x)
v(dx/dt)² + (dy/dt)² not an integral!
Limit as h approaches 0 of [f(a+h)-f(a)]/h
undefined


12. y = ln(x) - y' =

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13. slope of vertical line
negative
Limit as h approaches 0 of [f(a+h)-f(a)]/h
? v(1 + (dy/dx)²) dx over interval a to b
undefined


14. When f '(x) is decreasing - f(x) is...
use rectangles with right-endpoints to evaluate integrals (estimate area)
if integral converges - series converges
e^x
concave down


15. use integration by parts when...
Limit as x approaches a of [f(x)-f(a)]/(x-a)
positive
? f(x) dx integrate over interval a to b
two different types of functions are multiplied


16. left riemann sum
concave up
use rectangles with left-endpoints to evaluate integral (estimate area)
decreasing
uv - ? v du


17. Indeterminate forms
uv - ? v du
p ? 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
0/0 - 8/8 - 8*0 - 8 - 8 - 1^8 - 0° - 8°
f(x)


18. Volume of solid with base in the plane and given cross-section
? A(x) dx over interval a to b - where A(x) is the area of the given cross-section in terms of x
substitution - parts - partial fractions
negative
corner - cusp - vertical tangent - discontinuity


19. Alternating series tes
y' = sec(x)tan(x)
lim as n approaches zero of general term = 0 and terms decrease - series converges
? f(x) dx integrate over interval a to b
a^x ln(a)


20. When f '(x) is positive - f(x) is...
decreasing
two different types of functions are multiplied
increasing
use trapezoids to evaluate integrals (estimate area)


21. When f '(x) is increasing - f(x) is...
has limits a & b - find antiderivative - F(b) - F(a)
critical points and endpoints
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.
concave up


22. Eatio test
lim as n approaches 8 of ratio of (n+1) term/nth term > 1 - series converges
corner - cusp - vertical tangent - discontinuity
two different types of functions are multiplied
A function and it's derivative are in the integrand


23. Volume of solid of revolution - no washer
Limit as h approaches 0 of [f(a+h)-f(a)]/h
p ? r² dx over interval a to b - where r = distance from curve to axis of revolution
y' = 1/(1 + x²)
? v (dx/dt)² + (dy/dt)² over interval from a to b


24. Integral test
? v (dx/dt)² + (dy/dt)² over interval from a to b
if integral converges - series converges
p ? 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
Limit as x approaches a of [f(x)-f(a)]/(x-a)


25. y = cos?¹(x) - y' =

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26. definite integral
y' = 1/x
v(dx/dt)² + (dy/dt)² not an integral!
use rectangles with right-endpoints to evaluate integrals (estimate area)
has limits a & b - find antiderivative - F(b) - F(a)


27. Taylor series
polynomial with infinite number of terms - includes general term
y' = -csc²(x)
lim as n approaches 8 of ratio of (n+1) term/nth term > 1 - series converges
(uv'-vu')/v²


28. If g(x) = ? f(t) dt on interval 2 to x - then g'(x) =...
f(x)
y' = 1/x
concave down
concave up


29. rate
relative maximum
derivative
use ratio test - set > 1 and solve absolute value equations - radius = center - endpoint
? abs[v(t)] over interval a to b


30. y = tan?¹(x) - y' =

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31. When f '(x) changes fro positive to negative - f(x) has a...
two different types of functions are multiplied
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.
use ratio test - set > 1 and solve absolute value equations - check endpoints
relative maximum


32. methods of integration
y' = -csc²(x)
A function and it's derivative are in the integrand
y' = -1/v(1 - x²)
substitution - parts - partial fractions


33. y = cos²(3x)
y' = 1/(1 + x²)
two different types of functions are multiplied
chain rule
use to find indeterminate limits - find derivative of numerator and denominator separately then evaluate limit


34. y = ln(x)/x² - state rule used to find derivative
find first derivative - dy/dx = dy/dt / dx/dt - then find derivative of first derivative - then divide by dx/dt
Slope of secant line between two points - use to estimate instantanous rate of change at a point.
? A(x) dx over interval a to b - where A(x) is the area of the given cross-section in terms of x
quotient rule


35. absolute value of velocity
1/(b-a) ? f(x) dx on interval a to b
speed
velocity is positive
y' = 1/(1 + x²)


36. average value of f(x)
corner - cusp - vertical tangent - discontinuity
1/(b-a) ? f(x) dx on interval a to b
Alternating series converges and general term diverges with another test
relative maximum


37. Chain Rule

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38. dP/dt = kP(M - P)
Slope of secant line between two points - use to estimate instantanous rate of change at a point.
f(x) has a relative maximum
zero
logistic differential equation - M = carrying capacity


39. When f '(x) is negative - f(x) is...
y' = 1/v(1 - x²)
a^x ln(a)
decreasing
f '(g(x)) g'(x)


40. ? u dv =
v(dx/dt)² + (dy/dt)² not an integral!
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.
if lim as n approaches 8 of ratio of comparison series/general term is positive and finite - then series behaves like comparison series
uv - ? v du


41. Length of curve
p ? r² dx over interval a to b - where r = distance from curve to axis of revolution
y' = 1/x
y' = 1/v(1 - x²)
? v(1 + (dy/dx)²) dx over interval a to b


42. nth term test
polynomial with finite number of terms - largest exponent is 6 - find all derivatives up to the 6th derivative
if terms grow without bound - series diverges
decreasing
y' = 1/x


43. y = tan(x) - y' =

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44. use substitution to integrate when

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45. Given velocity vectors dx/dt and dy/dt - find total distance travelled
point of inflection
lim as n approaches 8 of ratio of (n+1) term/nth term > 1 - series converges
? v (dx/dt)² + (dy/dt)² over interval from a to b
polynomial with infinite number of terms - includes general term


46. trapezoidal rule
increasing
relative maximum
use trapezoids to evaluate integrals (estimate area)
uv' + vu'


47. area under a curve
y' = 1/v(1 - x²)
? f(x) dx integrate over interval a to b
increasing
if terms grow without bound - series diverges


48. Geometric series test
y' = sec²(x)
general term = a1r^n - converges if -1 < r < 1
use rectangles with left-endpoints to evaluate integral (estimate area)
y' = -csc²(x)


49. Given v(t) find total distance travelled
two different types of functions are multiplied
velocity is positive
? abs[v(t)] over interval a to b
a^x ln(a)


50. y = x cos(x) - state rule used to find derivative
relative minimum
p ? 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
a^x ln(a)
product rule