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Why does adding a constant to a function's input (as in f(x-a)) shift the plot of the function along the x-axis?

Imagine the function f(x) as a black box which takes in any value x and produces an output y. The black box acts on its input according to a rule which produces a unique value of y for a given x. If the b...

Answered by James H. • Maths tutor

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Solve the following definite integral: f(x)=3e^(2x+1) for the limits a=0 and b=1, leaving your answer in exact form.

First set up integral. Do not forget dx!

Int(f(x)) between 0 and 1

Optionally take out factor of 3 to simplify problem.

Solve using substitution and the exponential rule.

Integ...

Answered by Fraser B. • Maths tutor

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(x+2)(x-3)

Multiply the first term in the first bracket, so that would be x, with the second bracket. step one: x(x-3) is identical to: x^2 - 3x

We can now multiply the second number in the first bracket, whi...

Answered by Lai Wah T. • Maths tutor

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y = 4x^3 - 5/x^2 Find dy/dx

y = 4x^3 - 5/x^2 Easier to differentiate the 2nd term if it isn't written as a fraction so first rewrite y: y = 4x^3 - 5x^(-2) Then differentiate each term by multiplying each term by the current power of...

Answered by Nisha C. • Maths tutor

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Using the Trapezium rule with four ordinates (three strips), estimate to 4 significant figures the integral from 1 to 4 of (x^3+12)/4sqrt(x). Calculate the exact value of this integral, comparing it with your estimate. How could the estimate be improved?

Taking the value at the ordinates f(1) = 13/4, f(2) = 20/4sqrt(2), f(3) = 39/4sqrt(3), f(4) = 9.5 Then the trapezium rule states the integral is approximately 1/2 * [f(1) + 2f(2) + 2f(3) + f(4)], which (u...

Answered by Robert M. • Maths tutor

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