Q. 145.0( 1 Vote )

# Find the relation

Given, …(1)

It is given that f(x) is continuous at x = 3

By definition of continuity:

LHL at (x = 3) = RHL at (x = 3) = f(3) To relate ‘a’ and ‘b’ we can consider RHL = f(3), as calculation will be easier and fast and both the values will be related. You can take LHL = RHL also.  b(3+0) + 3 = 3a + 1

3b + 3 = 3a + 1

3a – 3b = 2 is the required relation.

OR

Given, xy = ex – y

Taking log both sides –

y log x = (x – y) loge e

y log x = x – y …(1)

x = y (1 + log x) = y log (xe) …(2)

y log x = x - y

Differentiating w.r.t x , we get – Applying product rule and chain rule of differentiation-    [ loge e = 1]  …[from eqn 1] …[putting the value of y/x form (2)]

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