Question

sinar13. lim

Answer 1

Let the function be

f( x )= sinax bx

We have to find the value of the function at Limit x→0

At a particular point x=0 , the function takes the form of 0 0

We have to simplify the term to remove 0 0 .form

According to trigonometric theorem,

lim x→0 sinx x =1 (1)

So, on dividing and multiplying the given function with ax we get

f( x )= sinax bx ⋅ ax ax = sinax ax ⋅ ax bx = sinax ax ⋅( a b )

Since the above expression is in standard form. Now on applying limits we get,

lim x→1 sinax ax .( a b )

As x→0 so ax→0 thus from equation 1:

lim ax→0 sinax ax .( a b )= a b lim ax→0 sinax ax = a b ⋅1 = a b (Taking constants outside the limit)

Thus the value of given expression lim x→0 sinax bx = a b