Top answers

It is given that f(x) = 2sinhx+3coshx. Show that the curve y = f(x) has a stationary point at x =-½ ln(5) and find the value of y at this point. Solve the equation f(x) = 5, giving your answers exactly

1.Differentiating: f'(x)= 2cosh(x)+3sinh(x) At a stationary point, we know f'(x)=0. Therefore 2cosh(x)+3sinh(x)=0. (easy to forget that unlike nromal trig there is no change in sign) Rearranging gives tanh(x...
SB
4823 Views

Integrate | x^7 (ln x)^2 dx ( | used in place of sigma throughout question)

Start the integration by parts process |udv = uv - |vdu u = (ln x) 2 dv = x 7 dx du = 2(ln x)/x dx v = 1/8 x 8 = 1/8 x 8 (ln x) 2 - | 1/4(ln x)x 7 dx = 1/8 x 8 (ln x) 2 -1/4 | x 7 (ln x) dx Repeat the integr...
RD
Answered by Rowan D. • Maths tutor
8616 Views

How would you structure a 6 mark essay question?

For a 6 marker, you should be developing 2 distinct points, totalling 4 marks, and then providing a well reasoned evaluation as a conclusion for the last 2 marks. For the two distinct points, it is important...
LH
Answered by Luke H. • Economics tutor
85818 Views

The area of a rectangle is 8cm^2. It has a length of (3x+1)cm and a width of (2x+5)cm. Work out the value of x.

We know that the equation of the area of a rectangle is width times by length. Therefore: 8=(3x+1)(2x+5) If we multiply out the brackets we get: 8=(6x 2 +2x+15x+5), thus, 8=6x 2 +17x+5, and therefore, 0=6x 2...
OC
Answered by Oliver C. • Maths tutor
12940 Views

What is an enzyme and explain the effect of two environmental factors on their efficiency?

Enzymes act as biological catalysts for reaction that occur in organisms such as animals and plants. This means that they help to speed up reactions, or allow them to take place at lower activation energy le...
OC
Answered by Oliver C. • Biology tutor
5131 Views