Maths Help Please?

Question

Could anyone help me on these two questions?

1. Convert into cartesian form

r(1 + sinANGLE) = a




Also

2. What is the largest possible domain and corresponding range for the function :

y = 1 + x + x^3

Any help on either would be appreciated

Cheers fellas, I really appreciate that!

Answer 1

2/4 *c =8

Answer 2

1. Convert into cartesian form
r(1 + sinANGLE) = a
r+rsinZ = a
But r sin Z = y and r sqrt(x^2+y^2)
So sqrt(x^2+y^2) +y = a
sqrt(x^2+y^2) = a - y
x^2 + y^2 = a^2 - 2ay + y^2
x^2 = a^2 - 2ay
2ay = a^2 -x^2
y= (a^2 -x^2)/2a

2. What is the largest possible domain and corresponding range for the function :

y = 1 + x + x^3
- infinity < x < +infinity is the domain. x can be any of the real numbers.
The range is infinity. y can have any value from - infinity to plus infinity.

Answer 3

2. y = 1 + x + x^3

For one thing, the largest possible domain would be all real numbers (as this is a property of polynomials to begin with). The range, however, is dependent on the absolute min/max values. Let's solve for those by finding the derivative.

y' = 1 + 3x^2

Setting y' to 0,

0 = 1 + 3x^2

This yields no solution. That means it is either always increasing or always decreasing. If we test any value for y' = 1 + 3x^2, you'll note that you get a positive result. Therefore, the function is increasing from (-infinity, infinity)