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How can do you factorize the equation x^2+6x+8

Here, we see that the term in x in the equation is 6, so we start by looking for a perfect square where the second term would be 6 : we get 6/2 = 3 so we try (x+3) 2. However, (x+3) 2 = x 2+ 6x + 9. We thus ...
MS
Answered by Marine S. • Maths tutor
3548 Views

Differentiate with respect to x, x^2*e^(tan(x))

Use the product rule: d/dx(uv) = uv' + u'v, with u = x^2 and v = e^(tan(x)), so that u' = 2x and v' = sec^2(x) * e^(tan(x)), and so the answer is 2x * e^(tan(x)) + x^2 * sec^2(x) * e^(tan(x)) .
JH
Answered by Jakub H. • Maths tutor
5752 Views

Using partial fractions, find f(x) if f'(x)=5/(2x-1)(x-3)

First step: partial fractions 5/(2x-1)(x-3) 5=A(x-3)+B(2x-1) A=0 when x=3, so B=5/(2x3-1)=1 B=0 when x=1/2, so A=5/(0.5-3)=-2 So f'(x)=1/(x-3)-2/(2x-1) Second step: Integration f(x)= (integral)(1/(x-3))dx - ...
JF
Answered by Jasmin F. • Maths tutor
5599 Views

When Integrating by parts, how do you know which part to make "u" and "dv/dx"?

you need to think about how the integral will be simpliefied, basically you are trying to get to a state where only one function of x resides in the integral. so if you have an x 2 sin3x dx inside the integr...
TG
Answered by Thomas G. • Maths tutor
4198 Views

A cubic curve has equation y x3 3x2 1. (i) Use calculus to find the coordinates of the turning points on this curve. Determine the nature of these turning points.

y′=3x2 −6x use of y′ = 0 0= 3x^2 - 6x 0= 3x(x-2) therefore either x=0 or x=2 when x=0 y=1, when x=2 y=-3 (0, 1) or (2, −3) y''=6x-6 when x=0 y''=6(0)-6 = -6 as y'' is negative this means at x=o the curve is ...
CB
Answered by Charlotte B. • Maths tutor
7933 Views