Limits

Question 1

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

x->a

Answer 1

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

Question 2

lim. f[g(x)]=

x->a

Answer 2

f { lim. g(x). }

x->a

Question 3

lim   sin(x-a)/(x-a) =
x->a

Answer 3

1

Question 4

lim tan(x-a)/(x-a)=
x->a

Answer 4

1

Question 5

lim sin^-1x/x =

x->0

Answer 5

1

Question 6

lim. tan^-1x/x =

x->a

Answer 6

1

Question 7

lim sin^-1x=

x->a

Answer 7

sin^-1a

Question 8

lim sinx•/x

x->0

Answer 8

||/180

Question 9

lim. cos^-1x =

x->a

Answer 9

cos^-1a

Question 10

lim. tan^-1x=

x->a

Answer 10

tan^-1a

Question 11

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

x->infinity

Answer 11

1

Question 12

lim. Log(1+x)/x =

x->0

Answer 12

1

Question 13

lim. Log(1-x)/x =

x->0

Answer 13

-1

Question 14

lim     Loga(1+x)/x =
x->0

Answer 14

Logae

Question 15

lim     Loga(1-x)/x =
x->0

Answer 15

-logae

Question 16

lim (e^x - 1)/x =

x->0

Answer 16

1

Question 17

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

x->0

Answer 17

Log a

Question 18

lim (e^₹x -1)/x =

x->0

Answer 18

₹

Question 19

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

x->a

Answer 19

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

Question 20

lim f(x)^g(x) =
x->a

Answer 20

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

Question 21

(1+x)^n =

Answer 21

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

If -1

Question 22

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

Answer 22

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

Question 23

Series of sin x

Answer 23

x - x^3/3! + x^5/5! - x^7/7! + …..

Question 24

Cos x=

Answer 24

1- x^2/2! + x^4/4! - x^6/6! +….

Question 25

tan x =

Answer 25

x = x^3/3 + 2/15x^5 + 17/315x^7+…

Question 26

Log(1+x)=

Answer 26

x- x^2/2 + x^3-3 - x^4/4 +…