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Mathematics: Post your doubts here!

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i need help with tan graphs...

sumone PLEASE provide me with notes or any explanation as to how to sketch them.
 
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i dont knw how to decide which sign to put wid inverse whn i get smthing lyk f-1 = +- √asd

if the given equation is too complex then change it to simple form as in complete square form
and when ur simplified equation turns to be like f(x) = -√2x
then ur f-1 (x) will be in the following way
f-1: x ----> divide by 2 -----> square ----> multiply by positive sign
i.e. f-1(x) = (x/2)^2
just oppose the process u will get ur inverse equation
 
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direction vector of line L is (1 -2 +2)
unit vector (n) of the plane P is also given (2 -3 +6)
now the cross product of these direction vector (1 -2 +2).(2 -3 +6) = (-6 -2 +1)
this wil be the direction vector of the line whose eq. is to be found out.

Now itx stated in the question that the line ahs a point A. we have already found out the position vector of that point "A"
make the q. of the line now. r = (3 +2 +1) +t(-6 -2 1) this is the eq. of the linE :)
 
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direction vector of line L is (1 -2 +2)
unit vector (n) of the plane P is also given (2 -3 +6)
now the cross product of these direction vector (1 -2 +2).(2 -3 +6) = (-6 -2 +1)
this wil be the direction vector of the line whose eq. is to be found out.

Now itx stated in the question that the line ahs a point A. we have already found out the position vector of that point "A"
make the q. of the line now. r = (3 +2 +1) +t(-6 -2 1) this is the eq. of the linE :)
thanks was just confused about which two vectors we were supposed to take for the cross product. Btw if i change the order for eg. (2-3+6).(1-2+2), the signs of the answer are different, i.e.(6+2-1), is this a big deal?
 
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p(x) has two roots
when factorised
p(x) = (x - 2) (2x^2 + x +2)
p(x) > 0
(x - 2) (2x^2 + x +2) > 0
Now we have to make a sketch, but the root (2x^2 + x +2) should first be checked if it has real roots
b^2 - 4ac = (1)^2 - 4(2)(2) = 1 - 16 = -15
That means no real roots and the whole curve lies above x-axis, never touches it
So the only point of p(x) that touches x-axis is x =2
(x - 2) (2x^2 + x +2) > 0
(x - 2) > 0
x > 2
 
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if the given equation is too complex then change it to simple form as in complete square form
and when ur simplified equation turns to be like f(x) = -√2x
then ur f-1 (x) will be in the following way
f-1: x ----> divide by 2 -----> square ----> multiply by positive sign
i.e. f-1(x) = (x/2)^2
just oppose the process u will get ur inverse equation
i knw hw to find an inverse but there is a negative sign for the root as well how do u choose...
 
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lets say f(x) = x^2 + 10 for x >= 0
thn f-1 = +- √(x) - 10
but this answr is wrong it can either be +√x or -√x
how to select ??

i think in this case the domain of f(x) has clearly mentioned that there is not inclusion of negative numbers of x so in inverse to there won't be any negative sign, only √x is accepted
m not pretty much sure about this.....
 
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y = A (x^n), natural log each side to get
ln y = ln A + n (ln x)
The gradient is n and y-intercept is ln A.
Just draw the line of best fit to find the two values. It should not be hard.
could u please explain q9 of 9709 may 2009 p3.
thanks
 
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e^x +e^2x=e^3x ( divide by e^x)
1 +e^x =e^2x ( substitute for e^x = u)
1 +u = u^2
u^2 - u -1 =0
u = 1 +square root ( -1^2 -4X 1 X -1) /2 X1
u = 1.62 ( the other u would be negative , so it is rejected)
e^x =1.62
x = ln (1.62 )=0.481
 
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thanks here's another one
direction vector of line L is (1 -2 +2)
unit vector (n) of the plane P is also given (2 -3 +6)
now the cross product of these direction vector (1 -2 +2).(2 -3 +6) = (-6 -2 +1)
this wil be the direction vector of the line whose eq. is to be found out.
Now itx stated in the question that the line ahs a point A. we have already found out the position vector of that point "A"
make the q. of the line now. r = (3 +2 +1) +t(-6 -2 1) this is the eq. of the linE :)


thanks was just confused about which two vectors we were supposed to take for the cross product. Btw if i change the order for eg. (2-3+6).(1-2+2), the signs of the answer are different, i.e.(6+2-1), is this a big deal?
 
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