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A curve C has the following equation: x^3 + 3y - 4(x^3)*(y^3) a) Show that (1,1) lies on C b) Find dy/dx

a) Substituting the coordinate (1,1) into the left hand side of the equation for C we obtain: (1 3 ) + 3*1 - 4(1 3 )(1 3 ) = 1 + 3 - 4 = 0 = The right hand side of the equation, hence the equation is satisfi...
HW
Answered by Harry W. • Maths tutor
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show that tan(x)/sec2(x) = (1/2)sin(2x)

tan(x)/sec 2 (x) Sec(x) = 1/cos(x), therefore 1/sec(x) = cos(x). also tan(x) = sin(x)/cos(x).using substitution, tan(x)/sec 2 (x) = (sin(x)/cos(x)) * cos 2 (x) = sin(x)cos(x). sin(x+y) = sin(x)cos(y) + cos(x...
OO
Answered by Olaitan O. • Maths tutor
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Differentiate 5x^2 + 11x + 5 with respect to x

The simple rule of thumb applied to differentiation can be used in this example - 'Multiply each term by its power then reduce the power by one'. Doing this 5x^2 becomes 2 5x^(2-1)=10x. Repeating for 11x giv...
SL
Answered by Sam L. • Maths tutor
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How do I know if I am using the right particular integral when solving a differential equation

Particular integrals will generally be derived in two different ways, depending on the type of the differential equation that you are solving. For example if it was a linear first order ODE, then you would h...
VV
Answered by Vaikkun V. • Maths tutor
11952 Views

Use the substitution u=4x-1 to find the exact value of 1/4<int<1/2 ((5-2x)(4x-1)^1/3)dx

We are required to solve this integral using integration by substitution, in which we assign a variable to equal a certain region of the integrated function in this case, 4x-1. The purpose of this is to remo...
TR
Answered by Taylor R. • Maths tutor
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