Calculate the taylor polynomials t2 x and t3 x centered at

Question

Problem 1

Find the formula for a function of the form y = A sin(Bx) + C with a maximum at (4, 3), a minimum at (12, -7), and no critical points between these two points.

Problem 2

Calculate the Taylor polynomials T₂ (X) and T₃ (X) centered at x = 2 for f(x) = ln(x + 1).

Problem 3

Use L'Hopital's Rule (possibly more than once) to evaluate the following limit

lim_t→0(12 sin(10t) ln(10t))

If the answer equals ∞ or -∞, write INF or -INF in the blank.