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Find the range of a degree-2 polynomial function such as 2x^2 +1, or x^2 + 2x - 3.

There are 3 methods for finding the range of a polynomial fucntion. This is good news because if you arrive at the same answer using these methods you wil be more confident that it is the correct answer.The ...
DH
Answered by Douglas H. • Maths tutor
3996 Views

What is the double angle formula?

The double angle formula is how to combine/split trigonometric functions so that they can be integrated or simplified using identities. For example, cos (a+b)= cos(a)cos(b) - sin(a)sin(b) , which can be exte...
RW
Answered by Robert W. • Maths tutor
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The finite region S is bounded by the y-axis, the x-axis, the line with equation x = ln4 and the curve with equation y = ex + 2e–x , (x is greater than/equal to 0). The region S is rotated through 2pi radians about the x-axis. Use integration to find the

formula for volume of solid generated = 2pi x integral between limits of y 2 expand ( e x + 2e -x ) 2 = e 2x +4+4e -2x integrate e 2x +4+4e -2x with respect to x= 1/2(e 2x ) + 4x - 2e -2x (+C) however c won'...
KT
Answered by Kit T. • Maths tutor
8004 Views

Integrate the function xsin(4x^2) with respect to x, using the integration by substitution method.

Heres our integral: int(xsin(4x 2 )dx)The first decision to make is what to use as our substitution. We're going to go for the term tied up in the sine function: 4x 2 Set u = 4x 2 du/dx = 8x, therefore dx = ...
BC
Answered by Benjamin C. • Maths tutor
4797 Views

Find the 1st derivative of y = x^2 + 7x +3 and hence find the curves minima.

Firstly, we differentiate y = x 2 +7x+3 . This gives dy/dx = 2x+7.The minimum value occurs when dy/dx = 0. So find x and y when dy/dx=0. 2x+7=0 implies x= -3.5, which from the first equation means y = (-3.5)...
CW
Answered by Connor W. • Maths tutor
4477 Views