Just need help on a few in each section to make sure Iâm doing it correctly! Thank you
taotion First think geometric series 4. Use substitution in a known series to find the Maclaurin's Series for the following functions. Be sure to include the interval of convergence in your answer. (a) f(z) =- (b) f(z) = ln(1-H) (c) f(z) = sin(2x) (d) f(z)=ea-2 5. Use term-by-term differentiation or integration of a known series to find a power series rep- resentation for each of the following functions. Be sure to include the interval of convergence in your answer. (a) f(z)=2cos(2x) (b) f(z) (c) f(z)=arctan(3x) (d) f(x)-In(1 +2x) 6x5 (e) f(z) = (14 6. Express the given parameterizations in the form y- f(x) by eliminating the parameter. (c) r(t) = ln(t), y(t)-3t + 2 (a) z(t) = 3e, y(t) = 7c" + 1 (b) () 6+t1, (t) 32 7. Find parametric equations for the segment joining the points P(L, 2) and Q(8,-4). 8. Use the formula for the slope of the tangent line to find for the curves: i. c(t) = (5e,22-7) at t-1. ti. c(t) = (3e, 2t + 2e-t) at t = 0.
