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A curve C is defined by the parametric equations x=(4-e^(2-6t))/4 , y=e^(3t)/(3t), t doesnt = 0. Find the exact value of dy/dx at the point on C where t=2/3 .

To solve this we must use the chain rule which is dy/dt * dt/dx. Firstly, we differentiate dy/dt. For this we must use the quotient rule, this gives us dy/dt=(9te^3t - 3e^3t)/9t^2. Now for dx/dt, by subst...

Answered by Lauren K. • Maths tutor

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Find the integral of tan^2x dx

You can not integrate tan²x but you can integrate sec²x Since sec²x = 1 + tan²x Then tan²

Answered by Nandini P. • Maths tutor

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How do i solve two linear simultaneous equations 2x+y=7 & 3x-y=8 ?

To start with, try and spot whether or not two of the coeffecients (numbers next to the letters) are the same for either question (i.e. could be a 3x in one equation and a 3x in the other). This also work...

Answered by Tom B. • Maths tutor

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Find the equation of the tangent to the unit circle when x=sqrt(3)/2 (in the first quadrant)

Unit circle: x² + y² = 1 when x = sqrt(3)/2: y² = 1 - (sqrt(3)/2)² y² = 1 - 3/4 y² = 1/4 y = 1/2 or -1/2 (first quadrant, so y is posi...

Answered by Kiran J. • Maths tutor

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Integral of (2(x^3)-7)/((x^4)-14x)

Set f(x)= (x^4)-14x. f’(x)=4(x^3)-14=2(2(x^3)-7). Thus we can write (2(x^3)-7)/((x^4)-14x)=(1/2)f’(x)/f(x). The integral of f’(x)/f(x)=ln|f(x)|+c. Thus the integral of (2(x^3)-7)/((x^4)-14x) is (1/2)(ln|f...

Answered by Issy K. • Maths tutor

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