This is a question from a past exam paper for entrance onto a degree course. Whilst I am sure that the question is not that difficult, I do have real problems with this type of question. I am not sure how to get started with part (a) so could you please list every step as simply as possible when solving the problem.

On part (b) (1) I have an answer although I am struggeling with finding what x is equal to in (2).

Could you also explain how to go about putting my answer in compound fractions?! and Integer?!

... for all n greater than or equal to 0. You can prove this without induction, just by simplifying the above formula and using the fact that 0! = 1. But, to prove...

... Proof. ... tanx −1 cos x− sin x− sinx cosx+cos2 xx(sinx+cos cosx xx 4. Solve the equation cossquaredx+2sinx+1=0 for the domain 0less thanor equal to x ...

The Lucas numbers L_n are defined by the equations L_1 = 1 and L_n = F_(n+1) + F_(n-1) for each n > or equal to 2. Prove that L_1 + 2L_2 + 4L_3 +8L_4 + ... ...

... x, y, z) in R3 for which the matrix xyz has rank 1 is the curve with parametric equations x = t, y = t2, z = t3 1 xy. 15. Prove: If k does not equal to zero ...

... subtraction, multiplication, division, or FOIL to prove that the ... The equal sign indicates that the left side is ... Hence, the equation is known as an identity. ...

... Find a formula for the number of handshakes, and prove the formula using induction. 5. Prove that any amount of postage greater than or equal to 12 cents can ...

... triangle opposite the right angle) is equal to the ... This equation provides a simple relation among the three ... Element , the Pythagorean theorem is proved by an ...

... Twice one angle is equal to the other angle plus the ... D. Solve the system of equations in part A to ... 3. There are more than 50 ways to prove the Pythagorean ...

...equation and realizing that both sides are not equal. ... to solve "Which integers meet the equation mxm = m + m?" and not necessarily a proof by contradiction. ...