Top answers

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
3966 Views

Use the geometric series formula to find the 9th term in this progression : 12 18 27...

Formula for nth term in a geometric progression = ar^n-1 workings: a=12 r=1.5 because 18/12 = 1.5 Thus, using ar^n-1 --> 12 * 1.5^8 = 307.54... or 308 (to 3sf) (In an ideal scenario question we'd be worki...
PF
Answered by Philip F. • Maths tutor
8948 Views

How would you show that a vector is normal to a plane in 3D space?

There are 2 main methods for finding a normal vector. If you know two vectors that lie in the plane e.g. (a,b,c) and (d,e,f), we can find a normal vector by calculating the vector/cross product of (a,b,c) an...
FK
Answered by Fionn K. • Maths tutor
29054 Views

Find the gradient of the exponential curve y(x)=(9e^(7x))/(12e^(2x)) at x=2/5

According to the quotient rule, when y(x)=f(x)/g(x), y'(x)=(f'(x)g(x)-g'(x)f(x))/g(x) 2 f(x)=9e 7x f'(x)=63e 7x , g(x)=12e 2x g'(x)=24e 2x y'(x)=(63e 7x .12e 2x -24e 2x .9e 7x )/(12e 2x ) 2 y'(x)=(756e 9x -2...
CM
Answered by Connor M. • Maths tutor
3582 Views

Use the double angle formulae and the identity cos(A+B)≡cos(A)cos(B)−sin(A)sin(B) to obtain an expression for cos 3x in terms of cos x only

To answer, you need to know and be able to use your trigonometric formulae including the double angle formulae on data sheet. 1: cos(3x)=cos(2x+x) = cos(2x)cos(x) - sin(2x)sin(x) split the 3x into two terms,...
SH
Answered by Sam H. • Maths tutor
18994 Views