One For You: Exponential Practice

1) Compute the values of sinh(x) and cosh(x) at x = 0; x = ln(2)(If you want, check this on Wolfram Alpha, but use exp(x) for ex)

2) Find where sinh(x) = 0 and where cosh(x) = 0

3) Show ex = cosh(x) + sinh(x); e−x = cosh(x) − sinh(x)

4) We know that 2 sin(θ) cos(θ) = sin(2θ). Is it true that 2 sinh(θ) cosh(θ) = sinh(2θ)?

5) We know that cos2(θ) − sin2(θ) = cos(2θ). Show cosh2(θ) + sinh2(θ) = cosh(2θ)?

6) let f(x) = xe−x2

a) Differentiate and Simplifyb) Differentiate y′ again, and simplify