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How do you go about sketching a curve when all you are given is the equation?

- First start by examining the equation. Is it in a recognisable form e.g. the equation of a circle/elipse etc. - If not, is it in the form y = or x = (these are the most common forms)? These are the steps y...
TS
Answered by Trishla S. • Maths tutor
3614 Views

Solve the equation 2ln2x = 1 + ln3. Give your answer correct to 2dp.

LHS: because alnx = lnx a , 2ln2x = ln(2x) 2 = ln4x 2 Now, because ln and e are inverse functions, we take both sides to the power of e. Therefore: e ln4x^2 = e 1 + ln3 4x 2 = e 1 + ln3 x 2 = (e 1 + ln3 ) / ...
SS
Answered by Shiv S. • Maths tutor
5261 Views

Integrate ⌠( xcos^2(x))dx

We must first use trigonometric identities to simplify cos 2 (x). We can use the formula cos(A+B) = cos(A)cos(B) - sin(A)sin(B) , where A=x and B=x , so that we get cos(2x) = cos 2 (x) - sin 2 (x) = 2cos 2 (...
DA
Answered by Daniel A. • Maths tutor
11096 Views

A curve C has equation y = (2 - x)(1 + x) + 3 . A line passes through the point (2, 3) and the point on C with x-coordinate 2 + h . Find the gradient of the line, giving your answer in its simplest form.

First we find the y coordinate which is a function of x: x = 2+ h so y = (2 - 2 - h)(1 + 2 + h) + 3 = -h 2 - 3h + 3 Now for the gradient, the line passes through points (2,3) and (2 + h, -h 2 - 3h + 3) dx = ...
RS
Answered by Ricardo S. • Maths tutor
4809 Views

How would you integrate ln(x) with respect to x?

Consider the function as 1(ln(x)) and then use integrating by parts, where you would differentiate the ln(x) part.
WC
Answered by William C. • Maths tutor
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