Limits Flashcards

1
Q

lim. [f(x)]^g(x). =

x->a

A

lim. g(x)
x->a
[lim. f(x) ]^
x->a

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

lim. f[g(x)]=

x->a

A

f { lim. g(x). }

x->a

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q
lim   sin(x-a)/(x-a) =
x->a
A

1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q
lim tan(x-a)/(x-a)=
x->a
A

1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

lim sin^-1x/x =

x->0

A

1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

lim. tan^-1x/x =

x->a

A

1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

lim sin^-1x=

x->a

A

sin^-1a

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

lim sinx•/x

x->0

A

||/180

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

lim. cos^-1x =

x->a

A

cos^-1a

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

lim. tan^-1x=

x->a

A

tan^-1a

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

lim. Sin(1/x)/(1/x)=

x->infinity

A

1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

lim. Log(1+x)/x =

x->0

A

1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

lim. Log(1-x)/x =

x->0

A

-1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q
lim     Loga(1+x)/x =
x->0
A

Logae

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q
lim     Loga(1-x)/x =
x->0
A

-logae

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

lim (e^x - 1)/x =

x->0

A

1

17
Q

lim. (a^x-1)/x =

x->0

A

Log a

18
Q

lim (e^₹x -1)/x =

x->0

A

19
Q

lim. [1 + f(x)]^1/g(x) =

x->a

A

e ^ lim f(x)/g(x)

20
Q
lim f(x)^g(x) =
x->a
A

e^lim[f(x)-1]g(x)

21
Q

(1+x)^n =

A

1 + nx + n(n-1)x^2/2! + n(n-1)(n-2)x^3/3! +…..

If -1

22
Q

(x^n - a^n)/(x-a) =

A

x^(n-1) + x^(n-2)a + x^(n-3)a^2 +…+a^(n-1)

23
Q

Series of sin x

A

x - x^3/3! + x^5/5! - x^7/7! + …..

24
Q

Cos x=

A

1- x^2/2! + x^4/4! - x^6/6! +….

25
Q

tan x =

A

x = x^3/3 + 2/15x^5 + 17/315x^7+…

26
Q

Log(1+x)=

A

x- x^2/2 + x^3-3 - x^4/4 +…