Please help me solve these problems:Show thatlimz0z2=0by an explicit - proof.13. Explain why the existence of the real limitslimx0f(x,0), and ,limy0f(0,y)does not guarantee that limz0f(z) exists. Give an example.14. Determine whether the following statement is true or false. Justify your answer:If f(z) is continuous at z0, then limzz0f(z) always exists and equals f(z0).15. Let f(z)=1z. Discuss the behavior of f(z) as z0 and as z. How is this related to the point at infinity on the extended complex plane?16. Letf(z)=z2x2+y2,z=x+iy,z0(a) Show that the limit as z0 does not exist.(b) Determine along which paths the limit exists, and what the values are.2.2 Homework: Limits of Complex FunctionsEvaluate the following limits, if they exist. If they do not exist, explain why.limz0sinzzlimz0|z|zlimziz2-(-1)z-ilimz1z2-1z-1limz0z(?bar(z))zlimz3z225z21limz1zlimz0z|z|For each of the following, approach along (i) the real axis, (ii) the imaginary axis, and (iii) the line y=mx. Determine whether the full limit exists.9.limz0z(?bar(z))10.limz0x2yx2y2,z=xiy11. Using the - definition, prove thatlimz2(3z1)=7.