Friday

April 18, 2014

April 18, 2014

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

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 12:41pmy^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 8:53amthank u so much for ur effort and time

helped me alot!!!!!

**Related Questions**

maths - given that y=1nx/x, x>0 (a) find the value of x for which dy/dx=0 (b...

maths - find equations for the tangent and the normal at P (1n2, 2k) on the ...

maths - find equations for the tangent and the normal at P (1n2, 2k) on the ...

calc - given S=piX(X+2Y) and V=piX^2Y show that dS/dX=pi(X-Y) when V is constant...

Calculus - The point (1,-2) is on the graph of y^2-x^2+2x=5. Find the value of (...

Maths Derivatives - If y = x ^ n + ( 1 / x ^ n ) prove that ( x^2y'' ) + ( xy...

Calculus - If x = t^2 + 1 and y = t^3, then d^2y/dx^2 = I know I can solve for t...

confused calc - dy/dx=2y^2 and if y=-1 when x=1, then when x=2, y=? (you already...

maths - If Y=(x^3+1)6, find d^2y/dx^2

Calculus - 2y^3 - 3xy = 4 1) Find dy/dx 2) Write an equation for the line ...