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a) Express 4(cosec^2(2x)) - (cosec^2(x)) in terms of sin(x) and cos (x) and hence b) show that 4(cosec^2(2x)) - (cosec^2(x)) = sec^2(x)

A) 4(cosec 2 (2x)) - (cosec 2 (x)) = 4/(sin 2 (2x)) - 1/(sin 2 (x)) = 4/[(2 sin(x) cos(x)) 2 ] - 1/(sin 2 (x)) B) 4/[(2 sin(x) cos(x)) 2 ] - 1/(sin 2 (x)) = 4/(4 sin 2 (x) cos 2 (x)) - 1/(sin 2 (x)) = 1/(sin...
MR
Answered by Mario R. • Maths tutor
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A curve has equation y = f(x) and passes through the point (4, 22). Given that f'(x) = 3x^2 - 3x^(1/2) - 7, use integration to find f(x), giving each term in its simplest form

As we are given the derivative of f(x), we first need to integrate this derivative to obtain the function, f(x). Using the standard integration formula, ∫ x^n dx = (1/n+1)(x^(n+1)) +c, integrate each term in...
AC
Answered by Alex C. • Maths tutor
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How do you integrate ln(x)?

Here, we use integration by parts. We must imagine ln(x) as a product of 1 and ln(x). We usually take the function of x to be our dv/dx, however, in the case of ln(x), we take that to be u (it is a special c...
OD
Answered by Omkar D. • Maths tutor
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Find the constant term in the expression (x^2-1/x)^9

This problem uses the binomial expansion formula: (x+y) n = k=0 Z n n C k x k y n-k .But lets try to understand where this formula comes from by doing the problem without it to start of with.We have the expr...
VY
Answered by Vincent Y. • Maths tutor
7953 Views

Differentiate: tan(2x) cos(x)

Explain the product rule : d/dx ( f(x) . g(x) ) = f'(x).g(x) = g'(x) . f (x) 2. Briefly run through trigonometric derivatives .* cos (x) differentiates to: -sin(x)* tan (x) differentiates to: sec^2 (x) 3. Br...
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Answered by Shreyasi D. • Maths tutor
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