solved Prove that 10^(n+1) + 3 * 10^n + 5 is divisible by 9 for n ∈ N
Question : Prove that 10^(n+1) + 3 * 10^n + 5 is divisible by 9 for n ∈ N Solution : We shall apply mathematical induction to Prove that 10^(n+1)…
Proved If H and K are subgroups of G then H ∩ K is a subgroup of G
Question : If H and K are subgroups of G then H ∩ K is a subgroup of G Solution : Let H and K are subgroups of G. Let…
how to Solve ut = kuxx (−∞ < x < ∞, 0 < t < ∞) u(x, 0) = e^(3x)
Question : how to Solve ut = kuxx (−∞ < x < ∞, 0 < t < ∞) u(x, 0) = e^(3x) Solution : To solve \[u_t\ \ =\ ku_{xx}\…
solution of the wave equation utt = c2 uxx for −∞ < x < +∞
Question : solve the wave equation utt = c2 uxx for −∞ < x < +∞ with the initial conditions u(x, 0) = φ(x)= sin x , ut(x, 0) =…
Find Real and Imaginary parts of the following complex numbers
Question : Find Real and Imaginary parts of the following complex numbersa) \[z = (2 + 3i)(−3 + 2i)\] b) \[z =\frac{4 + 2i}{3 − 4i}\]c) \[z = \bar{1 +…
solved Find general solution of the pde ut + ux = 0
Question : Find general solution of the pde ut + ux = 0 Solution :
how to determine first order pdes as linear homogeneous linear inhomogeneous or nonlinear
Question : how to determine first order pdes as linear homogeneous linear inhomogeneous or nonlinear Solution :
Question : If sec θ +tan θ =1/5. Find the quadrant in which θ lies and the value of sin θ
Question : If sec θ +tan θ =1/5. Find the quadrant in which θ lies and the value of sin θ Solution :
How many different ways could John buy an icecream and a cake?
Question : John wants to buy an icecream and a cake. There are four flavors of icecreams for sale, and sells five types of cake in three sizes. How many…
Using L Hospital s rule calculate lim(z→0) log^2((1+z)/z^2
Question : Using L Hospital s rule calculate lim(z→0) log^2((1+z)/z^2 Solution :