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i) Using implicit differentiation find dy/dx for x^2 + y^2 = 4 ii) At what points is the tangent to the curve parallel to the y axis iii) Given the line y=x+c only intersects the circle once find c given that c is positive.

I don't know how effectively I can communicate this answer via text without the whiteboard but I'll try. i) First implicitly differentiate with respect to x: 2x + 2y * dy/dx = 0. Rearranging gives dy/dx = -x...
JD
Answered by James D. • Maths tutor
5396 Views

Solve the simultaneous equations, 2x+y-5=0 and x^2-y^2=3

2x+y-5=0, y=5-2x (put into second equation) x 2 -y 2 =3, substituting in we get, x 2 -(5-2x) 2 =3, expand, x 2 -(25+4x 2 -20x)=3, simplify, x 2 -25-4x 2 +20x=3, 0=3x 2 -20x+28, put into brackets by seperatin...
JS
Answered by Joshua S. • Maths tutor
13021 Views

How do you differentiate 5x

y=5x The change in Y over the change in X gives the differential of 5x As the power of 'x' is 1, this is brought down and multiplied by 5 and the power of x is 1-1 = 0. Therefore, the power of x is 0, which ...
MM
Answered by Malik M. • Maths tutor
30236 Views

Differentiate x^x

x x =e x*ln(x) So d/dx (x x ) = d/dx (e x*ln(x) ) By chain rule, we get d/dx (xln(x)) e x ln(x) Then by product rule we get [ln(x)+1] e x ln(x)
MS
Answered by Matthew S. • Maths tutor
4624 Views

How many solutions are there to the equation sin x = a, if 0<a<1 and 0<x<pi

Draw the sine graph on a whiteboard. Infer graphically by drawing the line y = a. As 0
VN
Answered by Vedanth N. • Maths tutor
4156 Views