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 –   Rate this question :

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