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Why do you not add the 'plus c' when finding the area under a graph using integration even though you add it when normally integrating?

when integrating with the limits, you substitute in the two limits into the integral and then take them away. As both will have added the constant 'c', you are taking c away from c and so cancel out, so i...

Answered by Neha M. • Maths tutor

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For a given function F(x), what does the graph of the function F(x+2) look like in comparrison to F(x)?

F(x+2) is simply F(x) but whenever you see an 'x' replace it with 'x+2'. So when x is say 3, F(x) is F(3) and F(x+2) is F(5). If we draw this out on a graph, we see that this has the effect of shifting th...

Answered by James S. • Maths tutor

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Find the x-values of the turning points on the graph, y=(3-x)(x^2-2)

The minimum point occurs where dy/dx=0

We have 2 options: 1.) Expanding the brackets 2.) The product rule of differentiation

The shortest is the product rule: dy/dx= (d/dx)(3-x).(x²

Answered by Zita E. • Maths tutor

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The height (h) of water flowing out of a tank decreases at a rate proportional to the square root of the height of water still in the tank. If h=9 at t=0 and h=4 at t=5, what is the water’s height at t=15? What is the physical interpretation of this?

Note: time, t, is measured in minutes, and height, h, is measured in metres.

Let k>0, a constant.

The differential equation to be solved is given by: dh/dt = - k(h)^0.5.

Us...

Answered by Sandie N. • Maths tutor

4820 Views

curve C with parametric equations x = 4 tan(t), y=53^(1/2)sin(2t). Point P lies on C with coordinates (4*3^(1/2), 15/2). Find the exact value of dy/dx at the point P.

dy/dx = dy/dt *dt/dx (chain rule).

x=4tan(t) hence dx/dt = 4 sec²(t)

y = 53^1/2sin(2t) hence y'= 103^1/2 cos(2t)

therefore dy/dx = 103^...

Answered by Harry P. • Maths tutor

7464 Views

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Top answers

Why do you not add the 'plus c' when finding the area under a graph using integration even though you add it when normally integrating?

For a given function F(x), what does the graph of the function F(x+2) look like in comparrison to F(x)?

Find the x-values of the turning points on the graph, y=(3-x)(x^2-2)

The height (h) of water flowing out of a tank decreases at a rate proportional to the square root of the height of water still in the tank. If h=9 at t=0 and h=4 at t=5, what is the water’s height at t=15? What is the physical interpretation of this?

curve C with parametric equations x = 4 tan(t), y=53^(1/2)sin(2t). Point P lies on C with coordinates (4*3^(1/2), 15/2). Find the exact value of dy/dx at the point P.

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Search over 10,000 free study notes

Top answers

Why do you not add the 'plus c' when finding the area under a graph using integration even though you add it when normally integrating?

For a given function F(x), what does the graph of the function F(x+2) look like in comparrison to F(x)?

Find the x-values of the turning points on the graph, y=(3-x)(x^2-2)

The height (h) of water flowing out of a tank decreases at a rate proportional to the square root of the height of water still in the tank. If h=9 at t=0 and h=4 at t=5, what is the water’s height at t=15? What is the physical interpretation of this?

curve C with parametric equations x = 4 tan(t), y=5*3^(1/2)*sin(2t). Point P lies on C with coordinates (4*3^(1/2), 15/2). Find the exact value of dy/dx at the point P.

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© MyTutorWeb Ltd 2013–2025

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curve C with parametric equations x = 4 tan(t), y=53^(1/2)sin(2t). Point P lies on C with coordinates (4*3^(1/2), 15/2). Find the exact value of dy/dx at the point P.