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I’m having some trouble understanding functions. Mainly concerning how to know what the input and outputs are. Could you give me an explanation?

The best way to think about a function is to see it as a machine. Your input is the item you put into the machine, the function is what the machine does, and then when you get out of the other side is you...

Answered by Chelsie J. • Maths tutor

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

Heres our integral: int(xsin(4x²)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: 4x²Set u = 4x²

Answered by Benjamin C. • Maths tutor

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

Firstly, we differentiate y = x²+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 mean...

Answered by Connor W. • Maths tutor

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Find the value(s) of x which satisfies the equation 3x^2 + 6x + 3 = 0

First we must multiply the coefficient of x2 by the value with no x associated with it3x3 = 9Now we must find two numbers that add to make 6 and multiply to make 9+6x9 3 and 3Now we need to split the coef...

Answered by Jacob G. • Maths tutor

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The line L1 is given by the Equation y =3x+5, and the line L2 is given by the Equation 4y-12x+16=0. Show that the lines L1 and L2 are Parallel

Rewrite the equation for L2 to find an equation for y4y=12x-16; y = 3x - 4 2. The x-coefficient gives the gradient (or slope) of the line, so since the gradient of L1 is 3, and as we have just shown, the ...

Answered by William S. • Maths tutor

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