[CIE] All Pure Mathematics (P1, P2 and P3) doubts here !

[astarmathsandphysics]

the modulus question above - answer attacjed

[cs]

the modulus question above - answer attacjed

thanks! we can only use graph method for this question?

[cs]

dy/dx=(2xe^-x)-((x^2)(e^-x)) from part ii


let the tangent be y=mx

At point of intersection,

mx=(x^2)(e^-x)
after solving
m=0 or m=x(e^-x)

m=(dy/dx)
therefore,
x(e^-x)=(2xe^-x)-((x^2)(e^-x))
after solving,x=1

I think there is a short method which I don't now  


having doubt for this question too, thanks!

having doubt for this question too, thanks!

[astarmathsandphysics]

no you can also square both sides but I like the graph method cos it make the answer more obvious I think

[cs]

can you show me please, i cant get the answer using squaring both sides, sorry to bother you

[astarmathsandphysics]

By squaring both sides you sometimes get superfluous solutions with don't satisfy the problem. See attachment.

[cs]

By squaring both sides you sometimes get superfluous solutions with don't satisfy the problem. See attachment.

oh thank you, so its best to draw a graph

[astarmathsandphysics]

I think so. A quadratic has two solution (these may be the same) but one of them might not be a solution to the problem.

[curiousguy]

Please help me these questions its really urgent

[curiousguy]

Please help me with these questions its really urgent

[astarmathsandphysics]

here

[ashwinkandel]

Q.
(i)  Sketch the curve y = 2 sin x for 0 <= x <= 2pi. [1]
(ii) By adding  a suitable  straight  line  to your  sketch,  determine  the  number  of real  
      roots  of the equation
       2pi sin x = pi- x.
     State the equation  of the straight line. [3]

[Arthur Bon Zavi]

Q.
(i)  Sketch the curve y = 2 sin x for 0 <= x <= 2pi. [1]
(ii) By adding  a suitable  straight  line  to your  sketch,  determine  the  number  of real  
      roots  of the equation
       2pi sin x = pi- x.
     State the equation  of the straight line. [3]

What are the question marks ? Simply give year and the session.

[Sea Lover]

guys I need someone to explain to me this question ,it's in ocober /november 2010  varient 2 question 7(iii).
The function f is defined by
f(x) = x^2 ? 4x + 7 for x > 2.
The function g is defined by
g(x) = x ? 2 for x > 2.
The function h is such that f = hg and the domain of h is x > 0.
(iii) Obtain an expression for h(x).


In the markscheme the answer is x^2 +3, can someon explain it to me and how to get it?

[astarmathsandphysics]

f(x) = x^2 ? 4x + 7 for x > 2.

what does the question mark mean