Calculus Chapter 5 Test

Derivative of arccos

-1/sqrt(1-u^2)

Derivative of arctan

1/(1+u^2)

Average Value equation is

1/b-a (integral thingy) then equation; plug in then do b-a

Derivative of arcsin

1/sqrt(1-u^2)

g(x)

=(integral thingy) with equation

g''(x)

=f'(x)

g'(x)

=f(x)

"What is the average value of v on the interval...?"

Meaning: Average velocity in unit/time from t=whatever to t=whatever Solving: Solution for "how far does object travel" and multiply it by 1/b-a

"How far does the object travel for...?"

Meaning: Displacement of object in ft from t= whatever to t=whatever Solving: Take antiderivative of equation given, plug in t values given, subtract when plugged in b-a

Equation becomes what when multiplying by an extra x?

Odd; Cancels out so equals 0

"At what time would the object be traveling at avg velocity?"

Solve original given equation for t

"True or False? The object would travel the distance in part (whatever) at its average velocity from t=whatever to t=whatever?"

Solving: Multiply the highest x value by average velocity value and should equal displacement (minimum would be the displacement)

Odd Function

Symmetrical across origin

Even Function

Symmetrical across y-axis

"Do a reimann sum...Explain meaning of the integral"

Total displacement traveled in unit over time given

g(x) has a point of inflection when

f(x) changes from increasing to decreasing and vice versa

g(x) has a relative maximum when

f(x) changes from positive to negative

g(x) is concave down

f(x) is decreasing

g(x) is increasing when

f(x) is positive

Acceleration is positive when

v(t) is increasing

Average Velocity and "Find one approximation for the acceleration of the car" and use two close points (approximate derivative aka slope)

v(t2)-v(t1)/t2-t1