(4) Let f(x) (0 if x<0 (a) Show that f is differentiable at z (b) Is f'continuous on R? Is f continuous on R? Justify your answer.
IDY in < oo and lim - Yn < 0o. Prove that lim,+ 1. Let In > 0. Yn > 0 such that lim,- Yn) < lim,-- In lim,+ Yn: i tn < oo and lim yn < . Prove that lim. In 1. Let In 20, yn 0 such that lim Yn) < limn+In lim + Yr
Let Z be a standard normal random variable. Use the calculator provided, or this table, to determine the value of c. P(-csz<c)=0.9426 Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places. x 3 ? Let Z be a standard normal random variable. Use the calculator provided, or this table, to determine the value of c. P(0.55 <<c) -0.2624 Carry your intermediate computations to at least four decimal places. Round your answer to...
8,9,10 and 11. 8,9,10 are related with Bergman space. 8. If G zEC: 0<I2<13 show that every f in L2(G) has a removable singularity 9. Which functions are in L2(C)? 10. Let G be an open subset of C and show that if aeG, then (feL2(G): f(a)-o) 11. If {h.) is a seque at z=0. is closed in L(G). nce in a Hilbert space X such that Σ h, <00, then show that Σ-i hn converges in X.
2) Find the inverse z Transform of the following signal: 223-5z2+z+3 X(z) = (z-1)(z-3) [z] <1
2. Find all one-to-one analytic functions that map the upper half-plane U onto itself. (Hint: φ(z-i(1 + z)/(1-2) maps the unit disc onto U and φ is one-to- one.) 2. Find all one-to-one analytic functions that map the upper half-plane U onto itself. (Hint: φ(z-i(1 + z)/(1-2) maps the unit disc onto U and φ is one-to- one.)
Exercise 2. Let consider a normally distributed random variable Z with mean 0 and variance 1. Compute (a) P(Z < 1.34). (b) P(Z > -0.01). (c) the number k such that P(Z <k) = 0.975.
Given the logistic map Xn+1 = run(1 – Xn) with r > 0. Show the 2-cycle is stable for 3 <r <1+V6.
What is the output of the following? int sum=3, z=1; do { printf("The sum:%d*", sum+z); } while (sum<= 1); printf("0"); * 1 (2 Points) 40 4
Please explain every step! And please write clearly. Thank you! Let V be a the shape described by the following criteria in cylindrical coordinates: 0 < z <r, Find the average square of the distance from the origin of V.