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Find the equation of the tangent to the curve y = x^2-2x-3 at x=-1

First we find the gradient by differentiation. Differentiating the expression for the curve gives dy/dx=2x-2. Subbing in x=-1 gives dy/dx=-4 so the gradient of the line is -4.
To find the y intercep...

Answered by Caleb R. • Maths tutor

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evaluate the integral 2x/((9+x^2)^1/2) between -2 and 0

One approach would be to use integration by parts, as we have two functions of x within the integral. This approach would get you to the answer but would be more difficult and convoluted than necessary. O...

Answered by Aiden F. • Maths tutor

3226 Views

The height x metres, of a column of water in a fountain display satisfies the differential equation dx/dt = 8sin(2t)/(3sqrt(x)), where t is the time in seconds after the display begins. (a) Solve the differential equation, given that x(0)=0

Our DE (Differential Equation) dx/dt = 8sin(2t)/(3sqrt(x)) is separable because dx/dt can be expressed as a product of two functions of the form dx/dt = f(t)g(x) = (8sin(2t)) * (1/(3sqrt(x))).To solve the...

Answered by James M. • Maths tutor

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Derive double angle formulas from addition formulae

sin2x = 2sinxcosxcos2x = cos²x - sin²x=2 cos²x - 1= 1 - 2sin²xtan2x = (2tanx)/(1-tan²x)

Answered by Alexander H. • Maths tutor

3175 Views

Find the equation of the normal to the curve x^3 + 2(x^2)y = y^3 + 15 at the point (2, 1)

The first thing when seeing such a question is to find out what the question wants you to do and plan your method to do so.In this case, the question asks you to find the normal of a curv...

Answered by Kelvin L. • Maths tutor

3213 Views