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Find the coordinates of the minimum or maximum of the function f(x) = 3x^2 -2x +9 and determine if it's a minimum or maximum.

To find the minimum or maximum we need to find a point on the function where its slope is zero. So, we differentiate f(x) and set it equal to zero: f'(x)=0, f'(x) = 6x -2 = 0, x=1/3 Substitute into f(x) to g...
LB
Answered by Lilla B. • Maths tutor
1983 Views

Write down the expansion of (cosx + isinx)^3. Hence, by using De Moivre's theorem, find cos3x in terms of powers of cosx.

First, we expand by using binomial expansion (it is always helpful to draw Pascal's triangle to find each term's coefficients): 1 1 1 2 1 1 3 3 1 Since the function is raised to the power of 3, we use the un...
HF
Answered by Hiro F. • Maths tutor
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What is the limit for this function as x approaches 0? y(x)=(cos x)^(1/sin x)

When we try to simply compute y(0) we get 1 to infinity, which is indeterminate (we means we can either get 0, 1, infinity or God knows what else!). The way we want to approach these types of exercises is to...
Answered by • Maths tutor
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The sum of the first n terms of an arithmetic sequence is Sn=3n^2 - 2n. How can you find the formula for the nth term un in terms of n?

Having learned a lot about the arithmetic and geometric sequences, most people are used to expressing the n th term of a sequence un in the form u n =u 1 +d(n-1) for the arithmetic sequence and u n =u 1 *r n...
JP
Answered by Julianna P. • Maths tutor
16517 Views

Sketch the graph of x^2 - y^2 = 16

Before attempting to re-arrange the equation, we take an organic approach to looking at asymptotes:1) What happens to y when x=0 and when x -> infinity? What happens to x when y=0 and when y -> infinit...
Answered by • Maths tutor
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