struggling with some maths problems for study.
http://i.imgur.com/6HuOG.jpg
struggling with some maths problems for study.
http://i.imgur.com/6HuOG.jpg
I find some of the exponents too small for these old eyes to make out clearly...
Nevertheless, where are you stuck? Can you post what you have tried, or what your thoughts are on how to begin?
The problems are:
5) Differentiate
a) $\displaystyle f(x)= \frac{4}{x- 2}$
Looks like a simple application of the "quotient rule". Or, perhaps easier, write it as $\displaystyle f(x)= 4(x- 2)^{-1}$ and use the "chain rule".
b)$\displaystyle y= 40x ln(x^{2x+5})$
Using the fact that $\displaystyle ln(a^b)= bln(a)$ would simplify that a lot. Then just use the "product rule".
c) $\displaystyle V(t)= 10000e^{0.65x}$
Surely you know how to differentiate $\displaystyle e^x$? And, of course a very basic application of the "chain rule".
8)
a) Find the integrals of these functions
i) $\displaystyle f(x)= 9x^2+ x- 5$
Do you know that the integral of $\displaystyle x^n$ is [tex]\frac{x^{n+1}}{n+1}[tex]?
ii) $\displaystyle f(x)= 3e^x- 4x^2$
Do you know the itegral of $\displaystyle e^x$?
b) Find definite integral (i.e. area under the curve) of the above function for $\displaystyle 1\le x\le 5$ (i.e when x falls betweeen 1 and 5, inclusive).
Once you have done (a) this should be easy.
(For future reference, not making any attempt on these problems yourself, or even trying to type them in yourself, makes a very bad impression.)