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The graphs of functions f(x)=e^x and h(x)=e^(-.5x), where x is a real number and 0<x<1 ,lie on a plane. Draw these functions and find the area they and the line x=0.6 enclose using integration correct to 3 decimal places

∫ f(x)dx [.6, 0] - ∫ h(x)dx [.6,0]∫ f(x)dx = e^x....... f(x)dx [.6, 0] = (e^.6)-(e^0)=.822∫ h(x)dx = -2e^(-.5x)........... ∫ h(x)dx [.6,0]= (-2e^-.3)-(-2e^0)= .518.822 - .518= .304Therefore area enclosed ...

Answered by Brendan B. • Maths tutor

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Differentiate y = (3x^3+2x+7)/x^(1/2)

y = (3x^3+2x+7)/x^(1/2) = 3x^(5/2)+2x^(1/2)+7x^(-1/2)dy/dx = 15/2x^(3/2)+x^(-1/2)-3.5x^(-3/2)

Answered by Joshua W. • Maths tutor

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Given the function y = x^5 + x^3/2 + x + 7 Express the following in their simplest forms: i) dy/dx ii) ∫ y dx

i) 5x^4 + 3/2x^1/2 + 1ii) 1/6x^6 + 2/5x^5/2 + 1/2x^2 + 7x + c

Answered by Liam B. • Maths tutor

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Simplify 3/(x+1) + (3x-9)/2 = 1, to get a quadratic equation in the format ax^2 + bx + c = 0.

First, add the two fractions together. The common denominator is 2(x+1), or 2x+2. The first fraction becomes 6/(2x+2). The second fraction becomes (x+1)(3x-9)/(2x+2), or (3x²-6x -9)/(2x+2). Add...

Answered by • Maths tutor

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How do I know if a curve is convex?

The second differential of the equation of the curve will be positive if it is convex. This is because, by definition, convex means that the gradient of a curve is increasing. To find the gradient of a cu...

Answered by Josh W. • Maths tutor

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