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Find the gradient at the point (0, ln 2) on the curve with equation e^2y = 5 − e^−x . [4]

Figure out what skills are being tested: implicit differentiation and exponentials and logarithms.e^2y= 5 - e^-x2e^2y(dy/dx) = e^-x(dy/dx) = e^-x/ 2e

Answered by Theodore C. • Maths tutor

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There are 2 green jelly beans, 5 are yellow and 13 are red. Sue picks one jelly bean. What is the possibility that sue pick a jelly bean that is not yellow?

Answer: 3/4 2 green and 13 red therefore 15 of the 20 is not yellow simplifying this probability gives you 3/4.

Answered by Ann P. • Maths tutor

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Expand and and simplify (x^2 + 7) (x - 1)

Firstly, it is important to understand here that "expand" means multiply the two brackets. A logical approach can be taken to this question. Deal with the first term (x^2) of the first bracket: ...

Answered by Sherin T. • Maths tutor

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Find dy/dx when x+2y+3y^2= 2x^2+1

To solve this question we can use implicit differentiation. We can write:d/dx(x+2y+3y^2)=d/dx(2x^2+1).When differentiating something in terms of y with respect to x we can use the chain rule, this allows ...

Answered by Adam G. • Maths tutor

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A curve is given by the equation y=x^3-11x^2+28x; find the coordinates of the points where the curve touches the x-axis.

Since the equation has a cubic term, we can expect the curve to have certain properties: it should have three points where the graph touches the x-axis, two turning points, of which one should be a minimu...

Answered by Lui H. • Maths tutor

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