Most Important Selected Qs for JEE AdvancedMathematicsDifferentiation

If x=4 t^3+3, y=4+3 t^4 and ( d^2 x d y^2 ) ( d x d y )^n is a constant, then find the value of 4 5 + 4 5 n + 4 5 n^2 + . . upto infinity.

Correct answer

Step-by-step solution

aligned d x d y & = d x d t d y d t = 12 t^2 12 t^3 = 1 t d^2 x d y^2 & = d d t ( 1 t ) ( d t d y )= -1 t^2 1 12 t^3 = -1 12 t^5 ( d^2 x d y^2 ) ( d x d y )^n & = constant & n=5 Sum & = 4 5 1- 1 n = 4 5 1- 1 5 =1 aligned

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