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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
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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
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How many historians' opinions do I need to get an A*?

Your history exam is less about collecting the opinions of other historians and listing them, rather more about your ability to construct an argument whilst analysing alternative opinions. You should read ar...
RV
Answered by Robyn V. • History tutor
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Describe the role of RuBISCO in photosynthesis.

RuBISCO is an enzyme that is involved in the light independent reactions of photosynthesis, specifically, in the Calvin Cycle. This reaction takes place in the stroma. It catalyses the reaction of carbon dio...
CD
Answered by Claudia D. • Biology tutor
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Outline the structure and function of the plasma membrane

The plasma membrane is composed of a phospholipid by-layer. These phospholipid molecules are arranged in a double sheet which are stable yet fluid. These molecules have hydrophobic tails and hydrophilic head...
NL
Answered by Nathan L. • Biology tutor
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