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A curve has equation y = f(x) and passes through the point (4, 22). Given that f'(x) = 3x^2 - 3x^(1/2) - 7, use integration to find f(x), giving each term in its simplest form

As we are given the derivative of f(x), we first need to integrate this derivative to obtain the function, f(x). Using the standard integration formula, ∫ x^n dx = (1/n+1)(x^(n+1)) +c, integrate each term in...
AC
Answered by Alex C. • Maths tutor
8584 Views

Simplify fully: (24 - √ 300)/(4√ 3 - 5). Give your answer in the form a√ b where a and b are integers and find the values of a and b.

rationalise the denominator (remove the surds) by multiplying by a fraction = 1, known as the rationalising factor = (24 - √ 300)/(4√ 3 - 5) * (4√ 3 + 5)/(4√ 3 + 5) = (24 - √ 300)(4√ 3 + 5)/(48 - 25) = (24 -...
AL
Answered by Aloysius L. • Maths tutor
6761 Views

Solve the simultaneous equations. 2x + y = 18 . x - y = 6

x = 6 + y 2(6+y) + y = 18 12+2y+y = 18 3y = 18-12 3y=6 y = 6/3 = 2. So y = 2 if y = 2 then x is = ? x - y = 6 so, x-2 = 6 so x is 6+ 2 = 8 x = 8 and y = 2
OO
Answered by Olufunke O. • Maths tutor
3405 Views

How do you integrate ln(x)?

Here, we use integration by parts. We must imagine ln(x) as a product of 1 and ln(x). We usually take the function of x to be our dv/dx, however, in the case of ln(x), we take that to be u (it is a special c...
OD
Answered by Omkar D. • Maths tutor
4275 Views

Lottie has a bag of applies. She gives half of them to Fred. Fred eats two and then has four left. How many apples did Lottie have at the start?

General method 1. Write the information down in equation form defining unique symbols to represent the unknowns2. DOF analysis: Count the number of equations and unknowns? a. If #E = #U → unique solution b. ...
NG
Answered by Niraj G. • Maths tutor
5589 Views