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1)

 The number of points in (-, ) . for  which   x2xsinxcosx=0 is


A) 6

B) 4

C) 2

D) 0

Answer:

Option C

Explanation:

Concept involved

 The given equation contains algebraic  and trigonometric function called transcendal equation . To solve transcendal  equations we should  always plot the graph for LHS  and RHS

Here,   x2=xsinx+cosx

Let f(x)= x2  and   g(x) = x sin x+cos x

852021343_m3.JPG

 we know the graph for f(x)= x2

 To plot , g(x) = x sinx+cos x

 g'(x) = x cos x+sinx-sinx 

            g'(x)= x cos x   .....(i)

 g"(x) =- x sinx +cos x  ......(ii)

 put  g'(x)=0

        x cos x=0

          x=0,π2,3π2,5π2,7π2,....

at x=0,  3π2,7π2,....f"(x) >0

  minimum

   at x= π2,5π2,9π2,.... f"(x)<0

minimum

85202111_m4.JPG

      f(x) and g(x) are shown as

852021337_m5.JPG

    Number of solutions are 2.