limits continuity and differentiability

Question 1

formula 1

Answer 1

lim x^n-a^n/x-a=na^n-1

Question 2

formula of sin

Answer 2

lim sin x/x=1

Question 3

formula of tan

Answer 3

lim tan x/x =1

Question 4

formula of cos

Answer 4

lim 1-cosx/x^2=1

Question 5

FORMULA of e

Answer 5

e^x-1/x=1

Question 6

formula of a

Answer 6

a^x-1/x=log a

Question 7

formula of log

Answer 7

log(1+x)/x=1

Question 8

for infinite/infinite

Answer 8

l hopital or divide highest power

Question 9

for infiite-infinite form

Answer 9

rationalize

Question 10

existing of limit

Answer 10

lhl=rhl

Question 11

sin(x+y) =

Answer 11

sin(x)cos(y)+cos(x)sin(y)

Question 12

cos(x+y) =

Answer 12

cos(x)cos(y)–sin(x)sin(y)

Question 13

tan(x+y) =

Answer 13

(tan x + tan y)/ (1−tan x •tan y)

Question 14

sin(x–y) =

Answer 14

sin(x)cos(y)–cos(x)sin(y)

Question 15

cos(x–y) =

Answer 15

cos(x)cos(y) + sin(x)sin(y)

Question 16

tan(x−y) =

Answer 16

(tan x–tan y)/ (1+tan x • tan y)

Question 17

sin(2x) =

Answer 17

2sin(x) • cos(x) = [2tan x/(1+tan2 x)]

Question 18

cos(2x) =

Answer 18

cos2(x)–sin2(x) = [(1-tan2 x)/(1+tan2 x)]

Question 19

cos(2x) =

Answer 19

2cos2(x)−1 = 1–2sin2(x)

Question 20

Sin 3x =

Answer 20

3sin x – 4sin3x

Question 21

Cos 3x =

Answer 21

4cos3x-3cos x

Question 22

Tan 3x =

Answer 22

[3tanx-tan3x]/[1-3tan2x]

Question 23

a^2-x^2 or underroot a^2-x^2

Answer 23

x=asin@/acos@

Question 24

x^2-a^2 or underroot x^2-a^2

Answer 24

x= asec@/acos@

Question 25

a^2+x^2 or underroot a^2+x^2

Answer 25

x=atan@/acot@

Question 26

for continuity

Answer 26

LHL=RHL=F(A)

Question 27

for diffrentiabilty

Answer 27

RHD=LHD

every polynomial inverse trigno, exponential ,trigo eqn are continuos and diffrentiable