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Here, we must remember the definition of a bijection. To be bijective, a function must be both injective and surjective. For a function to be injective, we must have that f(a) = f(b) implies that a = b. For ...

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)...

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 < 4...

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...

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...