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Find the coordinate of the turning point of the curve y = x^2 - 10x + 7, by completing the square

First, we need to complete the square. We take the first part of the equation ignoring the constant ( + 7).  

y = x2 - 10x , we want to change the form of this equation from  x2

JP
Answered by James P. • Maths tutor
10157 Views

How do you integrate ln(x) with respect to x?

Rewrite ln(x) as 1ln(x) then integrate by parts.  The formula for integration by parts is ∫ uv' = uv - ∫ vu', here use u = ln(x) and v' = 1.  By differentiating u we get u' = 1/x, an...

AG
Answered by Anthony G. • Maths tutor
3374 Views

What is 2/3 + 1/4?

When adding or subtracting fractions, we must always start by putting the fractions over the same denominator, that is the number on the bottom half of the fraction. To do this, we need to find ...

CC
Answered by Catherine C. • Maths tutor
213152 Views

Differentiate the function f(x) = sin(x)/(x^2 +1) , giving your answer in the form of a single fraction. Is x=0 a stationary point of this curve?

The key concepts to apply in this question will be the product and chain rules, namely: if f(x)=g(x)h(h), then f'(x)=g(x)h'(x) + g'(x)h(x), and if h(x)=u(v(x)), then h'(x)=u'(v(x))v'(x). Equivalently, you...

BC
Answered by Bromlyn C. • Maths tutor
5386 Views

Show that: [sin(2a)] / [1+cos(2a)] = tan(a)

We start by expanding out the double trigonometric terms (sin(2a)) using the double angle formula, giving us: [2sin(a)cos(a)] / [1+cos^2(a) - sin^2(a)]. Next we spot that on the denominator (bottom half o...

GH
Answered by George H. • Maths tutor
9397 Views

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