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Calculus Flashcard Practice (Through plain trig derivatives) Flashcards | StudBud
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Calculus Flashcard Practice (Through plain trig derivatives)
Calculus Flashcard Practice (Through plain trig derivatives)
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1
\frac{d}{dx}\cos x=?
-\cos x
2\sin x\cos x
-\sin x
\sin x
2
\frac{d}{dx}\left(uv\right)=uv+u'v'
False
True
3
\tan\left(\frac{\pi}{2}\right)=?
1
undefined
\frac{\sqrt{3}}{2}
0
4
\sec\left(\frac{\pi}{6}\right)
1
\frac{1}{2}
\frac{\sqrt{3}}{2}
\frac{2}{\sqrt{3}}
5
\frac{d}{dx}\csc x=?
-\cot^2x
\sin x
-\csc x\cot x
\cos x
6
Alternate Definition of Derivative?
\lim_{x\to a}\frac{f\left(x\right)-f\left(a\right)}{x-a}
\lim_{x\to a}\frac{x-a}{f\left(x\right)-f\left(a\right)}
\lim_{x\to∞}f\left(x+h\right)-f\left(x\right)
\lim_{x\to0}\frac{f\left(x\right)}{x}
7
Definition of Derivative?
\lim_{h\to∞}\frac{f\left(x+h\right)-f\left(x\right)}{h}
\lim_{h\to0}\frac{f\left(x+h\right)+f\left(x\right)}{h}
\lim_{h\to-∞}\frac{f\left(x+h\right)-f\left(x\right)}{h}
\lim_{h\to0}\frac{f\left(x+h\right)-f\left(x\right)}{h}
8
What MUST be true to apply to the Intermediate Value Theorem (IVT)?
Neither
Continuous and Differentiable
Differentiable
Continuous
9
\frac{d}{dx}\sin x=?
-\sin x
\cos x\sin x
\cos x
\sec^2x
10
\frac{d}{dx}\sec x=\sec x\tan x
True
False
11
\frac{d}{dx}\tan x=\sec^2x
True
False
12
\frac{d}{dx}\cot x=
-\csc^2x
\cos x
\csc^2x
-\csc x\cot x
13
\frac{d}{dx}\frac{u}{v}=?
\frac{u'v-uv'}{v^2}
u'v+uv'
u'v-uv'
\frac{u'v+uv'}{v}
14
\sin\left(\frac{3\pi}{2}\right)=1
True
False
15
\frac{d}{dx}f\left(g\left(x\right)\right)=
f'\left(g\left(x\right)\right)g'\left(x\right)
f\left(g'\left(x\right)\right)
f'\left(g'\left(x\right)\right)
f\left(g'\left(x\right)\right)g'\left(x\right)
16
\lim_{x\to∞}\frac{\sin x}{x}=1
True
False
17
\frac{d}{dx}x^n
nx^{n-1}
nx^{n+1}
\frac{x^{n+1}}{n}
x^{n+1}
18
\log_ax=\frac{\ln x}{\ln a}
True
False
19
\sin\left(\frac{11\pi}{6}\right)=?
\frac{\sqrt{3}}{2}
-\frac{1}{2}
\frac{1}{2}
-\frac{\sqrt{3}}{2}
20
\cos\left(\frac{3\pi}{4}\right)
\frac{1}{2}
-\frac{\sqrt{2}}{2}
\frac{\sqrt{2}}{2}
1
