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(19x - 2)/((5 - x)(1 + 6x)) can be expressed as A/(5-x) + B/(1+6x) where A and B are integers. Find A and B

First we can equate (19x - 2)/((5 - x)(1 + 6x)) to A/(5-x) + B/(1+6x) which means:
(19x - 2)/((5 - x)(1 + 6x)) = A/(5-x) + B/(1+6x). Then we will turn the RHS into a single fraction:

(19x - 2...

Answered by Tarek S. • Maths tutor

2841 Views

Given that y = 8x + 2x^-1, find the 2 values for x for which dy/dx = 0

First differentiate y with respect to x, which gives you dy/dx = 8 - 2x^-2. This needs to equal zero so equate to zero. 8-2x^-2 = 0. You can then bring the 2x^-2 to the other side giving 2x^-2=8. Dividing...

Answered by Rosemary B. • Maths tutor

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Differentiate y = 4exp(6x) + cos(x) + 6x

dy/dx = 24e^6x - sin(x) + 6

Answered by Benn C. • Maths tutor

3882 Views

Express 2 cos x – sin x in the form Rcos( x + a ), where R and a are constants, R > 0 and a is between 0 and 90 ° Give the exact value of R and give the value of to 2 decimal places.

2cosx - sinx = Rcos(x+a) = Rcos(x)cos(a)-Rsin(x)sin(a)

Implying

2cos(x)=Rcos(x)cos(a)

Rcosa = 2

Similarly: Rsin(a) = 1

Therefore tan(a) = 1/2

Meaning a=26.57 Degr...

Answered by Thomas O. • Maths tutor

30481 Views

Integrate ln(x).

When tackling an unobvious integral question, first run through all the possible methods. I will now list the methods of integration: Substitution: could use this method, but it wouldn’t be particularly h...

Answered by Melanie C. • Maths tutor

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