AP Calculus (derivatives and limits) Flashcards

1

\frac{d}{dx}[\sin x+\tan x] = =\cos x+\sec x

False
True

2

lim f(5) =

= 4
= DNE
= 3
= 1

3

lim f(-1) =

= 2
= 1
= -2
= 0

4

lim f(4)

= -1
= 3
= DNE
= 4

5

\frac{d}{dx}=[3x^4+12x^{-2}+80^2]

=12x^{-3}+12^3+1600
=12x^4+24^{-2}+0
=12x^3+24x^{-3}+0
=12x^3+24x+0

6

\frac{d}{dx}[\frac{\sin x}{\tan x}]

\tan x(\sin x)-\sec^2x(\cos x)
\frac{\tan x(-\sin x)-\sec^2x(\cos x)}{(\tan x)^2}
\frac{\tan x(\sin x)-\sec^2x(\cos x)}{(\sin x)^2}
\frac{\tan x(\cos x)-\sin x(\sec x^2)}{(\tan x)^2}

7

lim f(2) =

= 1
= 3
= 2
= DNE

8

the limit of f(2) is 3

True
False

9

\frac{d}{dx}[(6x^3-x)^5]

=5(6x^3-x)(12^2-1)
=10(6x^3-x)(18x^2-1)
=5(6^3-x)(18x^2-1)
=10(6^4-x)(24^3-2)

10

\frac{d}{dx}[\frac{\cos x}{(2^x)^2}]

2x(\cos x)-\sin x(2^x)
\frac{2^x\left(-\sin x\right)-\cos x(2^x\ln2)}{(2^x)^2}
2x(\cos x)-\sin x(2^x)
\frac{2x(\cos x)-\sin x(2^x)}{(2^x)^2}

11

\frac{d}{dx}[4x^{-4}+3x^{10}+2x-4]

=16x^{-5}+30x^9-2
=16x^5+30x^{10}+2
=16x^{-5}+30x^9+2
=18x^{-4}+30x^{10}+2^x-4

12

The limit of f(6) is DNE

True
False

13

the derivative of \cot x is \csc^2x

False
True

14

is the derivative of \sec x is -\cos x

False
True

15

lim f(1) =

= DNE
= -2
= 1
= 2

16

\frac{d}{dx}=[e^{4x^{-3}}]

=e^{4x^{-3}}\cdot-12x^{-4}
=12x^{-4}
=e^{4x^{-3}}\cdot12x^{12}
=e^{4x^{-5}}\cdot40x^{-6}

17

the limit of -4 is 1

True
False

18

the derivative of 6^x is 6^x\ln6

True
False

19

lim f(2) =

= 3
= DNE
= -1
= 4

AP Calculus (derivatives and limits)

Questions 19

AP Calculus (derivatives and limits)

Questions 19