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The point A lies on the curve with equation y = x^(1/2). The tangent to this curve at A is parallel to the line 3y-2x=1. Find an equation of this tangent at A. (PP JUNE 2015 AQA)  

My exact explanation would depend on the students level of understanding. The following answer assumes a basic understanding of differentiation and equations of lines; a) Gradient of tangent is equal to grad...
SC
Answered by Sefret C. • Maths tutor
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How do you differentiate x^x?

To differentiate x x , we first let y = x x . ( Note that x x is not in the form x c where c is a constant or a x where a is a constant so the usual differentiation formulas cannot be used ). The trick here ...
AP
Answered by Anish P. • Maths tutor
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The straight line with equation y = 3x – 7 does not cross or touch the curve with equation y = 2px^2 – 6px + 4p, where p is a constant. Show that 4p^2 – 20p + 9 < 0.

The main piece of information this question gives us is that the two lines do not cross or touch. From this we can immediately see that we will need to use the discriminant of the quadratic formula b 2 - 4ac...
MW
Answered by Molly W. • Maths tutor
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Let f(x) = 2x^3 + x^2 - 5x + c. Given that f(1) = 0 find the values of c.

In order to solve this question we simply must substitute x=1 into f(x). If we carry out this substitution we see that f(1) = 2(1^3) + (1^3) -5(1) + c = 2(1) + (1) -5(1) + c = 2 + 1 - 5 + c = 3 - 5 + c = c -...
CL
Answered by Calum L. • Maths tutor
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sin(x)/(cos(x)+1) + cos(x)/(sin(x)+1) = 1

sin^2(x) + sin(x) + cos^2(x) + cos(x) = cos(x)sin(x) + cos(x) + sin(x) +1 (sin^2(x) + cos^2(x) =1) Therefore; 1 +sin(x) + cos(x) = cos(x)sin(x) + sin(x) +cos(x) +1 Cancelling out on both sides cos(x)sin(x) =...
JO
Answered by James O. • Maths tutor
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