Top answers

Find the volume of revolution about the x-axis of the curve y=1/sqrt(x^2+2x+2) for 0<x<1

The volume of revolution is given by integrating Pi y 2 dx from 0 to 1.Squaring, y 2 =1/(x 2 +2x+2)Completing the square, we see that y=1/((x+1) 2 +1)Make the substitution u=x+1, so du=dx. When x is 0, respe...
HG
3019 Views

Particles P and Q move in a plane with constant velocities. At time t = 0 the position vectors of P and Q, relative to a fixed point O in the plane, are (16i - 12j) m and -5i + 4j) m respectively. The velocity of P is (i + 2j) m/s and the velocity of Q

is (2i + j) m/s. Find the shortest distance between P and Q in the subsequent motion. This is an m4 question from the edexcel June 2015 paper. First I would explain to the student that I would form an equati...
3063 Views

For what values of x is Cosh^2(x) - Sinh(x) = 5 Give your answer in the form of a logarithm

Substitute Cosh^2(x) = 1 + Sinh^2(x) into the starting equation (This formula should be known)Make 0 the subject 3Sinh^2(x) - Sinh(x) - 2 = 0Substitute u = Sinh(x) and solve for uSubstitute Sinh(x) back in f...
LB
3072 Views

Using a Taylor's series or otherwise; derive Euler's Formula

Use the Taylor series expansion for the following three functions: f(θ) = e^(iθ), g(θ) = cos(θ) and h(θ) = sin(θ). We should find that f(θ) = e^(iθ) = 1 + iθ - (θ^2/2!) - i(θ^3/3!) + ... = Sum(θ^n/n!), g(θ) ...
MH
5441 Views

What is the root of i? give all solutions

Z=cos(PI/4) +sin(Pi/4) Z=cos(5PI/4) +sin(5Pi/4)
RS
3214 Views