What is the Statement for the Integral Evaluation Theorem AKA FTC 2?

IF F is any f^` of f(x), and f is continuous at every point [a,b], then..

\ln\left(a\right)+\ln\left(b\right)

\frac{d}{dx}\sec\left(x\right)

\tan\left(x\right)\sec\left(x\right)

Mr. Lee's velocity starts at 0. The continuous graph goes up 1, down 2, up 3, and down 2 from t= [0,4]. What do we know?

There is a Max/Min on [0,4], AND f(x) takes on every value f(0) to f(4).

Which Answer Equals 1?

\lim_{x\to0}\frac{\sin\left(x\right)}{x}

The Fundamental Theorem of Calculus(es) do what?

Links the concept of Diff a function with Integrating a function.

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AB Flash Cards 2024 - Lindsay, Arjun

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Questions 23

Answers

1
\frac{d}{dx}\csc^{-1}=
\frac{1}{|x|\sqrt{x^2+1}}
\frac{1}{|x|\sqrt{x^2+1}}
\frac{-1}{|x|\sqrt{x^2+1}}
\frac{-1}{|x|\sqrt{x^2-1}}
2
I go up, I go down, I go up again. What is my Displacement.
\int_a^bv\left(t\right)dt
\int_a^aa\left(t\right)dt
\int_b^av\left(t\right)dt
\int_b^ax\left(t\right)dt
3
What is the Statement for the Integral Evaluation Theorem AKA FTC 2?
IF f(x) is Cont EVERY point (a,b), and Diff [a,b], there is some value C...
IF f(x) is cont [a,b], then the function F(x)...
IF F is any f^` of f(x), and f is continuous at every point [a,b], then..
IF F is any f^` of f(x), and f is continuous at every point (a,b), then...
4
\frac{d}{dx}\left(uv\right)=
u'v+uv'
u'v'-u'v'
uv-uv'
u'v'+vu
5
ln(ab)
\frac{\ln x}{\ln a}
\frac{\ln a}{\ln x}
\ln\left(a\right)+\ln\left(b\right)
\ln\left(a\right)-\ln\left(b\right)
6
\frac{d}{dx}\int_6^{6x}\sqrt{t}dt
\sqrt{x}
\sqrt{6x}
6\sqrt{6x}
6
7
\lim_{x\to10}\frac{\frac{1}{x}-\frac{1}{10}}{x-10}
-\frac{1}{10}
Undefined
-\frac{1}{100}
\frac{1}{100}
8
\frac{d}{dx}\sec\left(x\right)
\tan\left(x\right)\sec\left(x\right)
1
-\csc\left(x\right)\cot\left(x\right)
2\sec\left(x^2\right)
9
Ms. Alves is moving to the parking lot from Math Class. When is she furthest away from the Parking Lot?
t=6
t=3
t=5
t=0
10
Derivatives calculate the vroom while acceleration is how much the vroom changes.
False
True
11
\frac{d}{dx}\sin\left(x\right)=
-\cos\left(-x\right)
\sin\left(x\right)
\frac{1}{1+\left(\tan x\right)^2}
\frac{1}{\sec\left(x\right)}
12
\sin\left(\frac{12\pi}{2}\right)\times\cos\left(10\pi\right)=?
0
\frac{\sqrt{3}}{2}
1
\frac{\sqrt{2}}{2}
13
Lord Farquaad has 6 Gingerbread Men at t=0. They bake at v(t) until t=6. What equation can find the amount at t=6?
6-\int_b^av\left(t\right)dt
\sqrt[3]{6+\int_a^ba\left(t\right)dt}
6+\int_b^av\left(t\right)dt
\int_a^bv\left(t\right)dt
14
The U in U substitution can be Substituted?
False
True
15
Mr. Lee's velocity starts at 0. The continuous graph goes up 1, down 2, up 3, and down 2 from t= [0,4]. What do we know?
f(x) takes on every value f(0) to f(4)
There is a Max/Min on [0,4], AND f(x) takes on every value f(0) to f(4).
The Domain of C is a set of all real numbers.
f\left(c\right)=\frac{f\left(4\right)-f\left(0\right)}{4-0}
16
Answer the Picture
1
-2 & 0
0 & 1
-2 & 1
17
Little Suzy wants to find the Half Life of a Radioactive Particle. What Equation could help them?
y=Ae^{kt}
f'\left(g\left(x\right)\right)\cdot g'\left(x\right)
\lim_{h\to0}\frac{f\left(x+h\right)-f\left(x\right)}{h}
\int_a^bf\left(x\right)=F\left(b\right)-F\left(a\right)
18
You are halfway through this Quiz
False
True
19
Which Answer Equals 1?
\lim_{x\to∞}\frac{\sin\left(x\right)}{x}
\lim_{x\to∞}e^x
\lim_{x\to0}\frac{\left(\cos\left(x\right)-1\right)}{x}
\lim_{x\to0}\frac{\sin\left(x\right)}{x}
20
The Fundamental Theorem of Calculus(es) do what?
Links Chain rule with the Gradient theorem
Links the concept of Diff a function with Integrating a function.
Links the Product rule to the Quotient rule.
Links the Squeeze theorem with Implicit Differentiation
21
Do you Like Calculus? Your teacher is NOT watching.
False
True
22
\lim_{x\to∞}\frac{6e^{4x}-e^{-2x}}{8e^{4x}-e^{2x}+3e^{-x}}
1
\frac{6}{8}
∞
\frac{3}{4}
23
\int_{ }^{ }a^x\ln\left(a\right)=
a^x
a^x+C
\pi\left(r\right)^2+C
e^x\ln\left(e\right)+C

AB Flash Cards 2024 - Lindsay, Arjun Flashcards | StudBud