Question

show that f(x) =cosx -cosbx if (x≠0) ½(b²-a²) if x=0 where a and b are real constants , is continuous at 0​

Answer 1

Answer:

x

2

cosax−cosbx

2

1

(b

2

−a

2

)

if

if

x



=0

x=0

where a and b are real constants, is continuous at 0.

Medium

Answer

RHL=LHL=

x→0

lim

x

2

cosax−cosbx

Using L's Hospital, we get

x→0

lim

2x

−asinax+bsinbx

Again Using L's Hospital, we get

x→0

lim

2

−a

2

cosax+b

2

cosbx

2

b

2

−a

2

Hence it is continuous at x=0 as RHL=LHL= value of f at x=0