Question

on dividing p(x) =9x⁴-4x²+4 by g(x)=3x²+x-x, the remainder ax-b then value of a and b is ​

Answer 1

Answer:

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Step-by-step explanation:

step 1 )

Let dy/dx =f₁(x) f₂(y) ..(1)

be given equation f₁(x) is a function of x alone and f₂(y) is a function of y alone.

step 2)

From (1) separating variables,

[1/f₂(y)] dy = f₁(x) dx ............(2)

step 3)

Integrating both sides of (2), we have ∫[1/f₂(y)] dy=∫f₁(x)dx + c...(3)

where c is constant of integration, is the required solution.

Note 1:

In all solution (3), an arbitrary constant c must be added in any one side only. If c is not added, then the solution obtained will not be a general solution of (1).

Note 2: To simplify the solution (3), the constant of integration can be chosen in any suitable form so as to get the final solution in a form as simple as possible. Accordingly, we are write log c, tan⁻¹ c, sin c, eᶜ,

(1/2). C , (-1/3). C etc in place of c in some solutions.

Note 3 :

The students are advised to remember by heart the following formulas. These will help them to write solution (3) in compact form

i) log x+ log y= log xy

ii) log x - log y = log(x/y)

iii) n log x = log xⁿ

iv)tan⁻¹x+tan⁻¹y= tan⁻¹[(x+y)/(1-xy)]

v) tan⁻¹x-tan⁻¹y = tan⁻¹[(x-y)/(1+xy)]

vi) eˡᵒᵍ ᶠ⁽ˣ⁾ = f(x).