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.
    I got (2x+5)e^(x^2-5x-1)+-2x/(x^2+1)^2 , if some mistake,please reply.
    sqrt(g(x))=(2x+5)0.5(x^2+5-1)^(-1/2) By chain rule

    2) a)At x=0,f(x)=2, so it is continuous. For the differentiate function of that, I am not sure because the function involve absolute value which I am sure how to differentiate an absolute value function.
    b) Not sure because the i do not know how to differentiate an absolute value function.

    Check answers, Thanks

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