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(x-3)(x-5)-(2a+1)/(a^(2))...

`(x-3)(x-5)-(2a+1)/(a^(2))`

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Use suitable identities to find the following products (i) (x +5) (x +2) (ii) (x-5) (x-5) (iii) (3x +3) (3x -2) (iv) (x ^(2) + (1)/( x ^(2)) )(x ^(2) - (1)/( x ^(2))) (v) (1+x) (1+x)

If y=x+(x^(3))/(3)+(x^(5))/(5)+…oo , show that (dy)/(dx)=(1)/(1-x^(2)) .

Knowledge Check

  • If 1/((x-2)(x-3))+1/((x-3)(x-4))+1/((x-4)(x-5))=1/6 , then the value of x will be :

    A
    8, -1
    B
    8, 1
    C
    `-8, 1`
    D
    `-8, -1`

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    Integrate each of the following functions w.r.t . X: (x^(3) - 4x^(2) + 5x - 1 )/((x-1)^(2))

    If y="tan"^(-1)(4x)/(1+5x^(2))+"tan"^(-1)(2+3x)/(3-2x) , prove that, (dy)/(dx)=(5)/(1+25x^(2))

    The power of x of the expansion [x+(x^(3)-1)^((1)/(2))]^(5)+[x-(x^(3)-1)^((1)/(2))]^(5) will be -

    Evaluate lim_(xtooo) ((7x^(2)+1)/(5x^(2)-1))^((x^(5))/(1-x^(3))).

    Prove that ""(1)/(2)cos^(-1)""((5cos x+3)/(5+3 cos x))= tan^(-1)""((1)/(2)tan""(x)/(2))

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