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 Apr 4 comment Prove $Tf$ is continuous, $T$ is a contraction and find a solution to the integral $f(x)$ How would I go about solving this equation? And is my answer to a.) correct? I think I have included some errors in my proof? Apr 4 asked Prove $Tf$ is continuous, $T$ is a contraction and find a solution to the integral $f(x)$ Apr 3 asked Which of the following sets are open (or closed)? Nov 17 awarded Commentator Nov 17 comment Evaluate the integral $\int_{\gamma}\frac{z^2+2z}{z^2+4}dz$ I've changed my partial fractions. Is this now correct? Nov 17 revised Evaluate the integral $\int_{\gamma}\frac{z^2+2z}{z^2+4}dz$ deleted 38 characters in body Nov 17 comment Evaluate the integral $\int_{\gamma}\frac{z^2+2z}{z^2+4}dz$ It's called Complex Analysis by Stewart and Tall. And I'll take another look at my partial fractions as they are incorrect. Nov 17 comment Evaluate the integral $\int_{\gamma}\frac{z^2+2z}{z^2+4}dz$ 'DepeHb': I think we're meant to use Cauchy's Integral Theorem. 'Git Gud': I can't say I am familiar with that definition. Is what I've done so far correct? And what would be the next logical step? Nov 17 comment Evaluate the integral $\int_{\gamma}\frac{z^2+2z}{z^2+4}dz$ Would that involve the Cauchy formula? Nov 17 asked Evaluate the integral $\int_{\gamma}\frac{z^2+2z}{z^2+4}dz$ Nov 8 awarded Tumbleweed Nov 1 awarded Editor Nov 1 revised Show that $\sum_{n=0}^\infty r^n e^{i n \theta} = \frac{1- r\cos(\theta)+i r \sin(\theta)}{1+r^2-2r\cos(\theta)}$ added 15 characters in body Nov 1 accepted Show that $\sum_{n=0}^\infty r^n e^{i n \theta} = \frac{1- r\cos(\theta)+i r \sin(\theta)}{1+r^2-2r\cos(\theta)}$ Nov 1 awarded Supporter Nov 1 asked Show that $\sum_{n=0}^\infty r^n e^{i n \theta} = \frac{1- r\cos(\theta)+i r \sin(\theta)}{1+r^2-2r\cos(\theta)}$ Feb 22 awarded Scholar Feb 22 accepted How do I sketch the following norms: Feb 22 comment Which of the following functions are norms? Not sure how to check the other two conditions though, would be it sufficient to assume that $A_3(x)$ is positive, i.e. $A_3(x)\geq 0$? Feb 22 comment Which of the following functions are norms? So for c.) I would check the scalar condition by $\parallel \lambda x\parallel=\parallel(\lambda x 1 ,\lambda x 2 )\parallel=\mid \lambda x 1 \mid+\mid\lambda x 2 \mid=\mid\lambda\mid \mid x 1 \mid+\mid\lambda\mid\mid x 1 \mid=\mid\lambda\mid(\mid x 1 \mid+\mid x 2 \mid)=\mid\lambda \mid\parallel x\parallel$.