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Arithmatic term n, Un= U1+(n-1)d. Where U1 is the first term of the sequence and d is the common difference. U5=U1+4d=6. U1=6-4d. Sum of arithmatic terms up to term n, Sn=n/2(2U1+(n-1)d). S12=12/2(2(6-4d)...

(a) In order to find the inverse of a function, it is easiest to swap x and y and solve for y. Here this would give, x=3y-5 => x+5=3y => (x+5)/3=y. Hence, f-1(x)=(x+5)/3. (b) Here it is important to...

Using the product rule (u'v+v'u, where u and v are the chosen substitutes) to find the first derivative will be dy/dx=x'=2xe^(-2x)+x^(2)e^(-2x)(-2)=2xe^(-2x)(x-x^2). This will give the d...

Recall that the general term in the binomial expansion of (x+y)^n is (nCr)(x^n-r)(y^r), so by the binomial theorem, the entire expansion is the sum of these terms from r = 0 to n. In this case, n = 33, th...

f(x)=(x³-2x)⁵
If we look at this function, we can see that it can be split into two functions, one hiding in the other one. Because of that, to solve this problem we will need t...