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Find the area bounded be the curve with the equation y = x^2, the line x = 1, the line x = -1, and the x-axis.

The answer is 2/3. This can either be obtained by performing a standard integration of y=x^2, using the power rule, between x = 1 and x = -1. Alternatively, integrate y = x^2 between x = 0 and x = 1, then do...
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Answered by Isaac A. • Maths tutor
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How do you sketch the curve y=(x^2 - 4)(x+3), marking on turning points and values at which it crosses the x axis

First, factorise the equation into y = (x+3)(x-2)(x+2), nothing that x 2 -4 is the difference of two squares so is easy to factorise. From the factorised equation, the points at which the curve crosses the x...
Answered by • Maths tutor
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The sum of the first K natural numbers is 300. Find the value of K.

S= 0.5n(n+1) ( formula for the sum of the first n natural numbers) 0.5K(K+1)= 300 ( sub in K and make the formula equal to the total sum given) 0.5K(K+1)-300= 0 ( take away 300 from both sides) 0.5K 2 + 0.5K...
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Answered by Meghan B. • Maths tutor
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The function f(x)=x^2 -2x -24x^(1/2) has one stationary point. Find the value of x when f(x) is stationary, and hence determine the nature of this stationary point.

dy/dx = 2x - 2 -12x -1/2 dy/dx = 02x - 2 - 12x -1/2 = 0x = 4 (stationary point)d 2 y/dx 2 = 2 + 6x -3/2 when x=4, d 2 y/dx 2 = 11/411/4 > 0 therefore the point is a minimum
Answered by • Maths tutor
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Take the 2nd derivative of 2e^(2x) with respect to x.

The second derivative is just two derivatives carried out back to back. In this case we just have to differentiate this function once, and then differentiate the result. The derivative of 2e^(2x) can then be...
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Answered by Patrick A. • Maths tutor
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