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Maths
A Level

The line PQ is the diameter of a circle, where points P and Q have the coordinates (4,7) and (-8,3) respectively. Find the equation of the circle.

Start by using the formula d = sqrt((x2-x1)2+(y2-y1)2)Therefore, substituting in our coordinates from P and Q:Length PQ = sqrt((-8-4)...

Answered by Matt C. Maths tutor
9285 Views

Prove that 2cot2x+tanx=cotx

2cot2x= 2(1/tan2x)= 2(1/(2tanx/1-tan2x))=2(1-tan2x)/2tanx= (1-tan2x)/tanx(1-tan2x)/tanx +tanx=(1-tan2x)/tanx +tan2x/tanx=1/tanx=cotx

Answered by Alisa D. Maths tutor
19212 Views

f(x)=ln(3x+1), x>0 and g(x)=d/dx(f(x)), x>0, find expressions for f^-1 and g

f^-1(x)=(e^x-1)/3 g(x)=3/(3x+1)

Answered by George K. Maths tutor
3792 Views

Differentiate [ x.ln(x)] with respect to x

The product rule is used to differentiate this since we are trying to differentiate the product of 2 parts--x and ln(x)So using the product rule which is d/dx=u.(dv/dx) +v.(du/dx)let u=x and v=ln(x)then d...

Answered by Omolola L. Maths tutor
3530 Views

Find the area enclosed by the curve y = 3x - x^2 and the x-axis

Start with finding limits by setting 3x - x^2 = 0, then factorise x(3 - x) = 0. Therefore x = 0 or 3. The area is the integral of 3x - x^2 between x = 0 and 3, sub in 3 and 0 into 3(x^2)/2 - (x^3)/3, whic...

Answered by Sam B. Maths tutor
16715 Views

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