Posted by **Yousef** on Friday, October 21, 2011 at 5:42am.

1) Find d^2y / dx^2 given that y^3 - x^2 = 4

2)If y = xª + ( 1 / xª ) , prove that

x^2 . y'' + xy' – a^2 . y = 0

3) Find dy/dx for the following function.

cos ( x - y ) = ( y ) ( 2x + 1 ) ^3

4)Find the values of A and B that make f(x) differentiable at

x = 0

f(x) = A + 2x + 3, if x > 0

AND

f(x) = 5 + B (sin²x / |x|) , if x < 0

- Maths Derivatives & Calulus -
**Steve**, Friday, October 21, 2011 at 12:41pm
y^3 - x^2 = 4

3y^2 y' - 2x = 0

y' = 2x/3y^2

6y y'^2 + 3y^2 y'' - 2 = 0

y'' = (2 - 6yy'^2)/3

= (2 - 6y(2x/3y^2)^2)/3

_______________

y = x^a + 1/x^a

y' = ax^(a-1) - a/x^(a+1)

y'' = a(a-1)x^(a-2) + a(a+1)/x^(a+2)

x^2 y'' = a(a-1)x^a + a(a+1)/x^a

xy' = ax^a - a/x^a

-a^2 y = -a^2 x^a - a^2/x^a

Add 'em up: 0

_______________

cos(x-y) = y(2x+1)^3

-sin(x-y)(1-y') = y'(2x+1)^3 + 6y(2x+1)^2

y'(sin(x-y) - y'(2x+1)^3 = xsin(x-y) + 6y(2x+1)^2

carry on

__________________

lim sin^2 x/x = 2sincos/1 = 0

f(0) = A + 3

f(0) = 5 + 0B = 5

So, if A=2, then the limit exists from both sides

- Maths Derivatives & Calulus -
**Yousef**, Saturday, October 22, 2011 at 8:53am
thank u so much for ur effort and time

helped me alot!!!!!

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