KiasuParents - Parenting in Singapore

KSP2013777 wrote:Thank you, Kenneth Tutor.
Can you help me with another question, Please?

Thank you.

The fraction is an improper fraction, since the degree of the numerator is 4 while the degree of the denominator is 3.

Perform long division first. You obtain x + (9 - 3x^2)/(x^3 + 3x)

Finally perform partial fraction decomposition on (9 - 3x^2)/(x^3 + 3x)

Final ans should be: x + 3/x - 6x/(x^2 + 3)

questionable_i wrote:Can anyone help me? in advance.

Q1) A function f is defined by f(x)=|x^2-3x|. Find the values of x for which f(x)=x-3.

Q2) Find the x-coordinates of the points of intersection of the curve y=|16-x^2| and the line y=33.

Q3) Find the x-coordinates of all the points at which the graph of y=|x^2-9|-5 meets the x-axis.

For Q1, first we sub one equation into another.

|x^2 - 3x| = x - 3

For modulus, there is the positive and negative side.

For the positive (and removing the modulus),

x^2 - 3x = x - 3
x^2 - 4x + 3 = 0
(x - 3)(x - 1) = 0

x = 3 or x = 1

For the negative,

x^2 - 3x = -(x - 3)
x^2 - 3x = -x + 3
x^2 - 2x - 3 = 0
(x - 3)(x + 1) = 0

x = 3 or x = -1

So the values of x are: -1, 1 or 3


You can use the same approach for Q2 and Q3. For Q3, the equation of x-axis is y = 0.

Please, can somebody help me solve this question?

Is it tangent to curve means Discriminant =0? But how to use Discriminant if there is ln x? Please help. Thank you

KSP2013777 wrote:Please, can somebody help me solve this question?

Is it tangent to curve means Discriminant =0? But how to use Discriminant if there is ln x? Please help. Thank you

this question is not about discriminant = 0. Always remember, discriminant is only for quadratic equation. This is a differentiation question.

So differentiatate and set dy/dx = gradient of the tangent. Find x. Then the y coordinate. Lastly the value of k. Give it a try. 加油。。

Thank you, piggy lalala. Can get my answer now.

I need help for this question. Can somebody please help me.

Thank you.

Can anyone help me with this question? Thank you.

1) By expressing each of the following equations in the form a^x=b where a and b are real numbers, take logarithms to solve for x.

(a) 2^(x+1)=3^x

(b)

KSP2013777 wrote:I need help for this question. Can somebody please help me.

Thank you.

questionable_i wrote:Can anyone help me with this question? Thank you.

1) By expressing each of the following equations in the form a^x=b where a and b are real numbers, take logarithms to solve for x.

(a) 2^(x+1)=3^x

(b)

Can somebody pls help me with this question?

Tks