# test review

1) let f(x)= $\frac{1}{x^2+1}$ and g(x)= x^2+5x-1

differentiate:

f(x)+g(x), f(x)*g(x), f(x)/g(x),( f(x))^g(x) and $\sqrt{g(x)}$

2) f(x)= $\frac{x+2}{1-|x|}$

a) evalute the continuity at x=0

b) Is the function derivable at x=0?

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### 1 Response to test review

1. NaiBing says:

Sorry for no latex, The latex tester don’t allow me to copy and paste at this time so I just type out.
f ‘(x)=-(x^2+1)^(-2)(2x) g'(x)=2x+5
So By differentiate:
f(x)+g(x)= (-2x)(x^2+1)^(-2) + 2x+5 By Sum rule
f(x)g(x)=-(x^2+1)^(-2)(2x) ( x^2+5x-1)+(1/(x^2+1))(2x+5) By product rule
f(x)/g(x)=(-(x^2+1)^(-2)(2x) ( x^2+5x-1)-(1/(x^2+1))(2x+5))/(x^2+5x-1)^2 By quotient rule
For f(x)^g(x) look complicated but I tried.And I am not sure it is right or wrong.