a) Evaluate the limit lim x→0 tan(2x) / x
b) Differentiate y = x^tan(x)
c) Find the equation of the tangent line to 4x^2 + 2xy−y^2 = 4
at the point (1, 2).
d) Differentiate f(x) = arctan(x^2 + 1)
e) Differentiate f(x) = ln(cosh x)
Thank you!
1. Find a closed form expression for the MacLaurin series for
f(x) = sinh(3x)
2. Find a closed form expression for the Taylor series for f(x)
= 4e2x expanded at a=3