Question

Find the value of the a and bif lim asinh x + bsin (x)/2x^3= 4/3 x-0 g co​

Answer 1

Answer:

Solution

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Using expansion,

x→0

lim

f(x)=

x→0

lim

x

3

(2x−

3!

(2x)

3

+...)+a(x−

3!

x

3

+...)+b(1−

2!

x

2

+...)

=

x→0

lim

x

3

(2+a)x−

2

bx

2

+x

3

(−

6

8

−

6

a

)+...

=finite

Above is posible only when 2+a=0

and b=0

∴a=−2,b=0 and limit is

−

6

8

−

6

a

=−

6

8

+

6

2

=−1.

Since the function is to be continuous therefore Limit=value

∴f(0)=−1.

Explanation:

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