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solve 4^xe^(7x+5) = 21

ln((4^x)e^(7x+5)) = ln21; apply a natural log on both sides of the equation as an exponential containing e is involved ln4^x + ln(e^(7x+5)) = ln21; using logarithm rules you can seperate the single log on th...
WN
Answered by Wahib N. • Maths tutor
3808 Views

How do you integrate y = 4x^3 - 5/x^2?

First we should look at the formula for integrating x n . The integral is (x n+1 / n+1) + C. Let's break down our equation into two parts. The integral of 4x 3 = 4(x 3+1 / 3+1) = 4(x 4 / 4) = x 4 The integra...
HJ
Answered by Hannah J. • Maths tutor
5331 Views

Find the Total Area between the curve x^3 -3x^2 +2x and the x-axis, when 0 ≤ x ≤ 2.

Initally this question appears to be a straightforward integration that should be carried out between the limits of x=0 and x=2. However if this process is carried out, as strange result is obtained: Area = ...
WK
Answered by Will K. • Maths tutor
11796 Views

Why do we get cos(x) when we differentiate sin(x)?

If we have an equation for a line, it follows a certain shape when put it on Cartesian axes. If we wish to find the value of the gradient of the graph at a certain coordinate, we can use differentiation to g...
SH
Answered by Sophie H. • Maths tutor
6964 Views

Prove that the lines 2y=3-x and y-2x=7 are pependicular.

We can find out whether lines are perpendicular by comparing their gradients. Each gradient should be the negative reciprocal of the other - for example, 3/2 and -2/3, or 4 and -1/4. (Writing the number as a...
PM
Answered by Pranavi M. • Maths tutor
4025 Views