for the MVT to be valid...

y must be cont. over closed and diff’ble over open interval

if you integrate velocity you get...

position, an A on your calc final

the main takeaway of the FTC is...

derivation is the inverse of integration

a definite integral is...

the signed area under the curve between points A and B

the IVT would state that the cont/diffble function f(x) of distance walked

would, if range is [1,11] and f(x)=0.5x, include x=22

a useless mess, h/3 (y0+4y1+2y2+4y3...4yn-1+yn)

if you derive acceleration you get

jerk, rate of change of the rate of change of the rate of change

how are riemann sums an integrals related?

a definite integral is a riemann sum with infinite subdivs

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a math quiz for S1 calc AB

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Questions 21

Answers

1
for the MVT to be valid...
y must be cont over closed and diff’ble over closed interval
y must be cont and diff’ble over open interval
y must be cont over open and diff’ble over closed interval
y must be cont. over closed and diff’ble over open interval
2
for a normal definite integral, you evaluate from _______ to get ________
b to a, F(a)-F(b)
a to b, F(b)-F(a)
b to a, F(b)-F(a)
a to b, F(a)-F(b)
3
if you integrate velocity you get...
jerk
acceleration
position
an A on your calc final
4
∫⁵₂1/x dx
-1/4 + 1/25
ln(2) - ln(5)
ln(5/2)
-1/25 + 1/4
5
the main takeaway of the FTC is...
derivation is the inverse of integration
you can solve derivatives with integrals
you can solve integrals by deriving the inside
calculus is calcuLIT
6
MRAM will ______ over a negative constant slope
be correct
underestimate
overestimate
7
a definite integral is...
the signed area between points A and B
the signed area under the curve
the area under the curve
the signed area under the curve between points A and B
8
derivative of arcsec(x)
1/(|x|√x2-1)
1/√x2+1
1/(|x|√x2+1)
oh frick off
9
when the accumulated positive area below a velocity graph is greater than the negative area...
the particle has moved left
the particle has moved right
the particle has stayed put
10
the function |x| _____ the MVT from [1,10]
does not contradict
contradicts
11
trapezoidal rule is...
h∕2 (y0+y1+y2........+yn)
h∕2 (y0+2y1+2y2........+yn)
h(y0+2y1+2y2........+yn)
h∕2 (2y0+2y1+2y2........+2yn)
12
the IVT would state that the cont/diffble function f(x) of distance walked
i don’t wanna come up with one more choice
would, if range is [1,11] and f(x)=0.5x, include x=.5
would, if f(x)=x2 and avg ROC=11, have f’(5.5) on domain
would, if range is [1,11] and f(x)=0.5x, include x=22
13
concavity occurs on the...
who cares?
an interval is an interval either way
closed interval
open interval
14
simpson's rule is...
a useless mess
h/3 (y0+2y1+2y2+2y3...2yn-1+yn)
3h (y0+4y1+4y2+4y3...4yn-1+yn)
h/3 (y0+4y1+2y2+4y3...4yn-1+yn)
15
if you derive acceleration you get
jerk
velocity
postion
rate of change of the rate of change of the rate of change
16
derivative of log_ax
1/(x*ln(a))
x/ln(a)
ln(a)/x
1/ln(x)
17
LRAM will ____ over a negative slope
overestimate
be correct
underestimate
18
derivative of csc(x)
-csc(x)cot(x)
csc(x)cot(x)
-csccot
csccot
19
how are riemann sums an integrals related?
a definite integral is a riemann sum with infinite subdivs
a riemann sum is a definite integral with A subdivisions
theyre almost always equal
they’re unrelated
20
which Riemann sum is most accurate on y=n where n is any constant
im dropping this class
RRAM
LRAM
21
derivative of cos²(x)
-sin2x
2cos(x)*sin(x)
sin2x
2sin2x

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