Calculus

Calculus

Limits Formulae :

✦

Lt

x→0

sinx=0.
✦

Lt

x→0

cosx=1.
✦

Lt

x→a

sinx=sin a, ∀ a∈R
✦

Lt

x→a

cosx=cosa, ∀ a∈R
✦

Lt

x→0

tanx=0.
✦

Lt

x→a

tanx=tana for a≠(2n+1)^π/₂; n∈Z..
✦

Lt

x→0

sinx

x

=1
✦

Lt

x→0

tanx

x

=1
✦ If n is a real number then i)

Lt

x→0

sinnx

x

=n ii)

Lt

x→0

tannx

x

=n
✦

Lt

x→0

1–cosx

x²

=¹/₂
✦

Lt

x→0

e^x–1

x

=1
✦

Lt

x→0

a^x–1

x

= log_ea
✦

Lt

x→∞

(1+

1

x

)^x=e
✦

Lt

x→ – ∞

(1+

1

x

)^x=e
✦

Lt

x→0

(1+x)^1/x=e

Differentiation Formulae :
✦

d

dx

{x}=1
✦

d

dx

{xⁿ}=nx^n–1
✦

d

dx

{√x}=¹/_(2√x)
✦

d

dx

{

ax+b

cx+d

}=

ad–bc

(cx+d)²

for x≠ –^d/_c
✦

d

dx

{e^x}=e^x
✦

d

dx

{a^x}=a^xloga
✦

d

dx

{logx}=¹/_x for x>0.
✦

d

dx

{sinx}=cosx
✦

d

dx

{cosx}= – sinx
✦

d

dx

{tanx}=sec²x for x≠(2n+1) ^π/₂, n∈Z.