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Use l’Hôpital’s rule to find lim(csc(x) - cot(x)) as x -> 0.

This question relies partially on remembering the trigonometric identities, csc(x) = 1/(sin(x)) and cot(x) = 1/(tan(x)) = cos(x)/sin(x). Plugging these values into the equation, we want to find Lim((1-cos(x)...
FS
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Given a^2 < 4 and a+2b = 8. Work out the range of possible values of b. Give your answer as an inequality.

For this question, we want to start by finding the possible values of a from the first equation and then using that to give us information about b from the second equation. Now, the condition that a^2 &lt; 4...
FS
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The first term of an infinite geometric series is 48. The ratio of the series is 0.6. (a) Find the third term of the series. (b) Find the sum to infinity. (c) The nth term of the series is u_n. Find the value of the sum from n=4 to infinity of u_n.

Note here: u_n indicates u subscript n. (a) u_1 = 48 and the ratio, r = 0.6 Using a calculator, u_2 = 48 x 0.6 = 28.8 u_3 = 28.8 x 0.6 = 17.28 (b) We have the known result that the sum to infinity of a geome...
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Answered by Felix S. • Maths tutor
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Express 0.545454... as a fraction in its simplest form.

First, we are going to give our decimal a name, let's call it x. We notice that x repeats after two digits, so how about we look at 100x. 100x = 54.54545454... But, the decimal part of this number is what we...
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Answered by Felix S. • Maths tutor
32104 Views

What is osmosis?

Osmosis is the movement of water from a high concentration to a low concentration through a partially permeable membrane . It is a special type of diffusion. You may get questions asking you to decide which ...
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Answered by Yvonne W. • Biology tutor
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