Finding value of c that makes function continuous

[AlexandraMarie112]

Homework Statement

f(x)= (sincx/x) ; x<0
1+(c)(tan2x/x) ; x≥0

Homework Equations

The Attempt at a Solution

Lim as x tends to 0+[/B] = 1+c⋅2⋅(sin2x/2x)⋅(1/cos2x) =1+c⋅2⋅1⋅1= 1+2c

Lim as x tends to 0 - = (sincx/x)=(c/1)⋅(sinx/x)=c⋅1=c

Equating both: 1+2c=c
c=-1

∴For the function to be continuous at x=0, c=-1

Is my answer correct?

 

[Mark44]

Homework Statement

f(x)= (sincx/x) ; x<0
1+(c)(tan2x/x) ; x≥0

Homework Equations

The Attempt at a Solution

Lim as x tends to 0+[/B] = 1+c⋅2⋅(sin2x/2x)⋅(1/cos2x) =1+c⋅2⋅1⋅1= 1+2c

Lim as x tends to 0 - = (sincx/x)=(c/1)⋅(sinx/x)=c⋅1=c

Equating both: 1+2c=c
c=-1

∴For the function to be continuous at x=0, c=-1

Is my answer correct?

Looks good to me.