Using L Hospital s rule calculate lim_(z→0)(1 – cos z)/sin^2(z)
Question : Using L Hospital s rule calculate lim_(z→0)(1 - cos z)/sin^2(z) Solution:
Calculate the derivative of e^(z^2)
Question : Calculate the derivative of e^(z^2) Solution: Given function h(z) = e^(z^2) Put w=f(z) =z^2 and g(w)=e^w then h(z)=g(f(z)) Here h(z) = g(f(z)) is the composition of functions f(z)…
how do you find the zeros of cos z
Question : Find the zeros of cos z Solution : zeros of cos z are obtained by solving cos z = 0 Put cos z = (e^(iz) + e^(−iz))/2 e^(iz)…
Question: Prove that f(z) = e^z is differentiable at any point z
Question: Prove that f(z) = e^z is differentiable at any point z Solution: Given complex values function f(z) = e^z Put z =x+iy f(z) = e^z=e^(x+iy)=e^x e^(iy) f(z) = e^z…
solved Show that f(z) = |z|^2 is differentiable only at z=0
Question : Show that f(z) = |z|^2 is differentiable only at z=0 Solution : Given complex function f(z) = |z|^2 = z z ̅ Since z= x+iy and z ̅= x-iy, i^2=-1…
Show that f(z)=conjugate(z) has no derivative
Question : Show that f(z)=conjugate(z) has no derivative Solution : We know that a complex conjugate finction is defined as f(z)= z ̅=x-iy Then Re f(z) = u(x, y) = x…
solved Find the Laplace transform of t^n
Question: Find the Laplace transform of t^n Solution :
solved Find the Laplace transform of the constant function
Question: Find the Laplace transform of the constant function Solution :
Question : Find equilibrium points of dy/dt =0.0625y-0.0005y^2 and plot solution curves
Question : Find equilibrium points of dy/dt =0.0625y-0.0005y^2 and plot solution curves that satisfy y(0)=1 and y(0)=10 Solution : Where red and green curves are solution curves of the ode…
how to plot slop field of y’=-y/x
Question : Plot the slop field of y'=-y/x for -10<=x<=10, -10<=y<=10 Solution : Matlab program to plot slope field of ode y'=-y/x, in -10<=x<=10,-10<=y<=10 n = 20;a= -10; b =…