Question

plz answer this question ​

Answer 1

Function is continous at x= 0

Limx->0. sin 5 x)/ 3x

sin( 5 x). × 5x)/ 5x. × 1/3x

As sin 5x)/ 5x. = 1

So

5x /3x = 5/3

So k= 5/3

✌✌✌Dr.Dhruv✌✌✌✌✌

Answer 2

Heya

_______________________________

FOR A FUNCTION TO BE CONTINUOUS LEFT HAND LIMIT IS EQUAL TO RIGHT HAND LIMIT IS EQUAL TO VALUE OF FUNCTION

AT x = 0

R.H.L

lim Sin5x / 3x
x—>0+

=>

lim { Sin5x / 5x } × 5x/3x
x—>0+

=>

lim 5x/3x
x—>0+

= 5/3

L.H.D

lim { Sin5x / 5x } × 5x/3x
x—>0-

=>

lim 5x/3x
x—>0-

= 5/3

lim = k
x—>0

FOR A CONTINUOUS FUNCTION

5/3 = 5/3 = k

=>

k = 5/3