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Let Sn be the sum of the first n terms of the arithmetic series 2 + 4 + 6 + ... i) Find S4

Firstly look for key terms in the question, identifying that we are going to be finding the sum of n terms, and it is an arithmetic series . This allows us to know which equations to look for in our formula ...
SL
Answered by Sydney L. • Maths tutor
6517 Views

The quadratic function f(x) = p + qx – x^2 has a maximum value of 5 when x = 3. Find the value of p and the value of q.

Express the quadratic equation using the formula that uses the vertex (x and y of the minimum/ maximum value). The formula is f(x)=a(x-h)^2 + k, where h=-b/2a and k=f(h). Now we have that a=-1 from the probl...
RN
Answered by Rafik N. • Maths tutor
13201 Views

How to find the derivative of sqrt(x) from first principles?

Graphical explanation leading to the expression that we need to develop (Lim(a->0) (sqrt(x+a) - sqrt(a))/(a). Then we need to understand how to rearrange a fraction involving square roots (multiplication ...
OD
Answered by Olivier D. • Maths tutor
2255 Views

log8(5) = b. Express log4(10) in terms of b

log 8 5=b using the base change rule log 8 5 = log 4 5/ log 4 8 log 4 8 can be solved: log 4 8 =x 4 x =8 2 2x = 2 3 2x=3 x= 3/ 2 Therefore we can write: log 8 5 = log 4 5/( 3/ 2) =b log 4 5 =( 3/ 2) b [1] To...
BM
Answered by Beatrice M. • Maths tutor
10710 Views

Given 2x^2-3y^2=2, find the two values of dy/dx when x=5.

First solve for the exact point on the line by substituting 5 into the original equation. You should get y=+-4. Now implicitly differentiate the equation: 4x-6y(dy/dx)=0. Rearranging this will yield the foll...
KU
Answered by Kalid U. • Maths tutor
7703 Views