AP Calculus AB

Concepts used: Derivatives with logarithmic equations Derivatives with trig and inverse trig Integration rules Applications of calculus Finding volume with integration

Flashcards27 cardsFPractice quizPHost liveL

Questions 27

Answers

1
\int_{ }^{ }a^xdx=\frac{a^x}{\ln a}+c
True
False
2
\frac{d}{dx}\sin^{-1}x=
-\frac{1}{1+x^2}
-\frac{1}{\sqrt{1-x^2}}
-\frac{1}{|x|\sqrt{x^2-1}}
\frac{1}{\sqrt{1-x^2}}
3
\frac{d}{dx}\arctan x=
-\frac{1}{\sqrt{1-x^2}}
\frac{1}{\sqrt{1-x^2}}
\frac{1}{1+x^2}
-\frac{1}{1+x^2}
4
\int_{ }^{ }\frac{1}{\sqrt{x^2-1}}dx=
arctanx+c
arccosx+c
arcsinx+c
\sec^{-1}x+c
5
\int_{ }^{ }\frac{1}{1+x^2}dx=
arctanx+c
\sec^{-1}x+c
arccosx+c
arcsinx+c
6
\frac{d}{dx}\ln x=
\ln x
\frac{1}{\ln x}
\frac{1}{x}
a^x
7
\int_{ }^{ }\sec^2xdx=
tanx+c
secxtanx+c
-tanx+c
-secxtanx+c
8
\frac{d}{dx}\tan x=
\sec^2x
\frac{1}{\cos^2x}
\sec x\tan x
\sin^2x
9
\int_{ }^{ }\frac{1}{x}dx=\ln|x|
False
True
10
\frac{d}{dx}\csc x=
\cos x
\sec^2
-\csc x\cot x
\csc x\cot x
11
\frac{d}{dx}\sin x=
\cos x
\tan x
\sin x
-\cos x
12
\frac{d}{dx}\log_ax=
\frac{1}{x}
a^x
\frac{1}{x\ln a}
\ln x
13
\frac{d}{dx}\cot x=
\csc x
\tan x
\cos^2x
-\csc^2x
14
\frac{d}{dx}\sec^{-1}x=
-\frac{1}{\sqrt{1-x^2}}
\frac{1}{\sqrt{1-x^2}}
\frac{1}{|x|\sqrt{x^2-1}}
-\frac{1}{|x|\sqrt{x^2-1}}
15
\int_{ }^{ }\frac{1}{|x|\sqrt{x^2-1}}dx=
arccosx+c
arcsinx+c
\sec^{-1}x+c
arctanx+c
16
\int_{ }^{ }\csc^2xdx=
-cscx
-cscx+c
-cotx+c
-cotx
17
\frac{d}{dx}\cos x=
-\sin x
-\left(-\sin x\right)
-\cos x
\sin x
18
\frac{d}{dx}e^x=e^x
False
True
19
\int_{ }^{ }\sec x\tan xdx=\sec x+c
True
False
20
\frac{d}{dx}\sec x=
\sec x\tan x
-\csc^2x
\cot x
-\csc x\cot x
21
\frac{d}{dx}\csc^{-1}x=
-\frac{1}{\sqrt{1-x^2}}
\frac{1}{|x|\sqrt{x^2-1}}
\frac{1}{\sqrt{1-x^2}}
-\frac{1}{|x|\sqrt{x^2-1}}
22
\int_{ }^{ }\sin xdx=-\cos x+c
False
True
23
\frac{d}{dx}\csc x=
\sec^2
\csc x\cot x
-\csc x\cot x
\cos x
24
\int_{ }^{ }\cos xdx=-\sin x+c
False
True
25
\frac{d}{dx}a^x=
lna
axlna
ax
axlna
26
\int_{ }^{ }\csc x\cot xdx=
cotx+c
-cscx+c
cscx+c
tanx+c
27
\frac{d}{dx}\cos^{-1}x=
\frac{1}{\sqrt{1-x^2}}
\frac{1}{1+x^2}
-\frac{1}{\sqrt{1-x^2}}
\frac{1}{|x|\sqrt{x^2-1}}

AP Calculus AB Flashcards | StudBud

AP Calculus AB

27 termsStudBud Administration15 plays

Concepts used: Derivatives with logarithmic equations Derivatives with trig and inverse trig Integration rules Applications of calculus Finding volume with integration

Flashcards27 cardsFPractice quizPHost liveL

Questions 27

Answers

1
\int_{ }^{ }a^xdx=\frac{a^x}{\ln a}+c
True
False
2
\frac{d}{dx}\sin^{-1}x=
-\frac{1}{1+x^2}
-\frac{1}{\sqrt{1-x^2}}
-\frac{1}{|x|\sqrt{x^2-1}}
\frac{1}{\sqrt{1-x^2}}
3
\frac{d}{dx}\arctan x=
-\frac{1}{\sqrt{1-x^2}}
\frac{1}{\sqrt{1-x^2}}
\frac{1}{1+x^2}
-\frac{1}{1+x^2}
4
\int_{ }^{ }\frac{1}{\sqrt{x^2-1}}dx=
arctanx+c
arccosx+c
arcsinx+c
\sec^{-1}x+c
5
\int_{ }^{ }\frac{1}{1+x^2}dx=
arctanx+c
\sec^{-1}x+c
arccosx+c
arcsinx+c
6
\frac{d}{dx}\ln x=
\ln x
\frac{1}{\ln x}
\frac{1}{x}
a^x
7
\int_{ }^{ }\sec^2xdx=
tanx+c
secxtanx+c
-tanx+c
-secxtanx+c
8
\frac{d}{dx}\tan x=
\sec^2x
\frac{1}{\cos^2x}
\sec x\tan x
\sin^2x
9
\int_{ }^{ }\frac{1}{x}dx=\ln|x|
False
True
10
\frac{d}{dx}\csc x=
\cos x
\sec^2
-\csc x\cot x
\csc x\cot x
11
\frac{d}{dx}\sin x=
\cos x
\tan x
\sin x
-\cos x
12
\frac{d}{dx}\log_ax=
\frac{1}{x}
a^x
\frac{1}{x\ln a}
\ln x
13
\frac{d}{dx}\cot x=
\csc x
\tan x
\cos^2x
-\csc^2x
14
\frac{d}{dx}\sec^{-1}x=
-\frac{1}{\sqrt{1-x^2}}
\frac{1}{\sqrt{1-x^2}}
\frac{1}{|x|\sqrt{x^2-1}}
-\frac{1}{|x|\sqrt{x^2-1}}
15
\int_{ }^{ }\frac{1}{|x|\sqrt{x^2-1}}dx=
arccosx+c
arcsinx+c
\sec^{-1}x+c
arctanx+c
16
\int_{ }^{ }\csc^2xdx=
-cscx
-cscx+c
-cotx+c
-cotx
17
\frac{d}{dx}\cos x=
-\sin x
-\left(-\sin x\right)
-\cos x
\sin x
18
\frac{d}{dx}e^x=e^x
False
True
19
\int_{ }^{ }\sec x\tan xdx=\sec x+c
True
False
20
\frac{d}{dx}\sec x=
\sec x\tan x
-\csc^2x
\cot x
-\csc x\cot x
21
\frac{d}{dx}\csc^{-1}x=
-\frac{1}{\sqrt{1-x^2}}
\frac{1}{|x|\sqrt{x^2-1}}
\frac{1}{\sqrt{1-x^2}}
-\frac{1}{|x|\sqrt{x^2-1}}
22
\int_{ }^{ }\sin xdx=-\cos x+c
False
True
23
\frac{d}{dx}\csc x=
\sec^2
\csc x\cot x
-\csc x\cot x
\cos x
24
\int_{ }^{ }\cos xdx=-\sin x+c
False
True
25
\frac{d}{dx}a^x=
lna
axlna
ax
axlna
26
\int_{ }^{ }\csc x\cot xdx=
cotx+c
-cscx+c
cscx+c
tanx+c
27
\frac{d}{dx}\cos^{-1}x=
\frac{1}{\sqrt{1-x^2}}
\frac{1}{1+x^2}
-\frac{1}{\sqrt{1-x^2}}
\frac{1}{|x|\sqrt{x^2-1}}