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Show that the integral of tan(x) is ln|sec(x)| + C where C is a constant.

First, recall that tan(x) can be rewritten in terms of sine and cosine. tan(x) = sin(x)/cos(x) The rephrasing of our question suggests that we should try the substitution rule of integration. We should subst...
AS
Answered by Anja S. • Maths tutor
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Solve the inequality 4x^2​>5x-1

We first rearrange the inequality to obtain 4x 2 -5x+1>0 Initially we approach this as if it were 4x 2 -5x+1=y, looking for y=0 We then look for solutions, the most general way is to use the quadratic for...
CL
Answered by Christopher L. • Maths tutor
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How do I plot y=x^2-1?

To plot any graph, you need to find out where the curve cuts the x and y-axis, and where it's stationary points are, aswell as what type of stationary point you have. Here are the steps: 1) Let x=0; find whe...
LP
Answered by Laura P. • Maths tutor
6489 Views

A curve is described by the equation x^3 - 4y^2 = 12xy. a) Find the points on the curve where x = -8. b) Find the gradient at these points.

a) The first part of this question is asking us to find points, (x,y), such that x = -8. By taking the equation and substituting in x = -8, we should find values, y, such that the points given are (-8,y). (-...
BC
Answered by Ben C. • Maths tutor
16662 Views

What are the roots of 3x^2 + 13x + 4 ?

To find the roots, we solve the equation 3 x 2 + 13x + 4 = 0. We could try factorising the equation, which gives us (3x + 1)(x + 4) = 0 So the roots are x = -1/3 and x = -4. Alternatively, we could use the q...
NB
Answered by Nicholas B. • Maths tutor
11190 Views