Q. 165.0( 4 Votes )

Find the value of

Answer :

Given,


…(1)


As, f(x) is continuous at x = 0


Left hand limit(at x = 0) = RHL(at x = 0) = f(0)



To find the value of k we can consider LHL = f(0), as calculation will be easier and fast. You can take any other consideration.



{using equation 1}




As limit is taking 0/0 form so we need to rationalize the expression.



Using (a+b)(a-b) = a2 – b2 and applying algebra of limits


We have-






-k = 1


k = -1


OR


Given,


As x = acos3 θ …(1)


Differentiating x w.r.t θ we get-



{using chain rule}


…(2)


Similarly we have,


y = a sin3 θ …(3)


Differentiating y w.r.t θ we get-




{using chain rule}


…(4)


By chain rule we can write that:



{from 2 and 4}




Again differentiating w.r.t x we get –




From equation 2 we have –





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