Top answers

Integrate the function f(x)=3^x+2 with respect to x

First note that a=e ln(a) and ln(a b )=b ln(a)By substituting a=3 x we get a=3 x =e ln(3^x) =e x ln(3) , and hence f(x)=e x ln(3) +2∫ f(x)dx=∫ e x ln(3) +2 dx . First we can split this into the sum of two in...
CC
Answered by Christian C. • Maths tutor
3552 Views

Find the maximum value of 2sin(x)-1.5cos(x)

Put the equation in the form Rsin(x-a) (=Rsin(x)cos(a)-Rcos(x)sin(a)). Looking at the original equation Rcos(a) = 2 and Rsin(a) = 1.5. Tan(a)=1.5/2 and R^2= 2^2 +1.5^2. Therefore R = 2.5 and a = 0.6435.The m...
TA
Answered by Tom A. • Maths tutor
8944 Views

Given that y = cos(3x)cosec(5x), use the product rule to find dy/dx.

Write out the product rule: if y=f(x)g(x) where f and g are functions, dy/dx = f'(x)g(x) + f(x)g'(x) Substitute in the expressions from the question:Therefore if f(x)=cos(3x) and g(x) = cosec(5x), f'(x) = -3...
HL
Answered by Harry L. • Maths tutor
4101 Views

How do you find the equation of a tangent to a curve at a certain point, from the equation of the curve?

First thing you would do is write down the coordinates where the tangent meets the curve. After that you would differenciate the equation (f(x)) of the curve (do dy/dx) in order to get f'(x).Then you would s...
AO
Answered by Antoine O. • Maths tutor
4159 Views

John wants to separate a rectangular part of his garden for his puppy. He has material for a 100-meter long fence and he plans to use one side of his house as a barrier. How should John select the sizes of his fence in order to gain the biggest territory?

We can denote the sides of the rectangle with a and b. As one side of the separated area is going to be the wall of the house, we do not have to use a fence there. Therefore, we will have two sides, one deno...
SG
Answered by Soma G. • Maths tutor
3413 Views