The integral from 0 to 1 of 6/x-1 dx
If I am correct, the answer guide says this one converges but my answer is going to infinity which is diverges. I need to see your steps to compare with mine please.
1.) Use residues to evaluate the improper integral from 0 to infinity:
1 / (x^2 + 1)^2 dx
2.) Use Jordan's Inequality to evaluate the improper integral from -infinity to infinity:
(x^3 sin ax) / (x^4 + 4)
Thank you for your assistance.
Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the given interval. (Round you answer to four decimal places. Enter your answers as a comma-separated list.)
f(x)= 8 times sq.rt x, [4,9]
(1) let f:C----R be an analytic function such that f(1)=1. Find the value of f(3)
(2) Evaluate the integral over & of dz/ z^2 -1 where & is the circle |z-i|=2
(3)Evaluate the integral over & of (z-1/z) dz where & is the line path from 1 to i
(4) Evaluate the integral between 2pi and 0 of
e^-i@ . e ^e^i@ d@
1.) Show that the functions f1(x)=5^x, f2(x)=5^(x-3), ans f3(x)=5^x + 3^x all grow at the same rate as x approaches infinity.
2.) Determine whether each integral converges or diverges.
a.) integral from 0 to 2 of (dx)/(4 - x^2)
b.) integral from 0 to infinity of (5 + cosx) e^(-x)dx
c.) integral from 0 to in
a). Show that the line integral ∫_C▒〖ysinxdx-cosxdy〗 is independent of the path.
b). evaluate the integral in part (a) along the line segment from (0, 1) to (π,-1)
c). Evaluate the integral ∫_((0,1))^((π,-1))▒〖ysinxdx-cosxdy〗 usingTheorem 16.3.1 and confirm the value is the same as that obtained in part
Could you please help explain these problems?:
16. Find the least non-negative residue of:
(i) 5^18 mod 11;
(ii) 4^47mod 12;
28. Show that 11 divides 10a+b if and only if 11 divide a - b. Use this to show that 11 divides 232595.
30. Find the lease non-negative residues mod 7, 11 and 13 of 58473625.