Q. 145.0( 1 Vote )

Find the relation

Answer :

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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