MATH 140 Lecture 24: All Formulas

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.

Need Help?ReWalch Talk to a Tulb /1 points sCalcET8 3.4.007 Find the derivative of the function Fx) (3x6 + 4x3)4 F(x) = Need Help? Resd it Watch It Talk to a Tutor +1 points SCalcETS 3 4.009 Find the derivative of the function. f(x) = v 9x + 8 f (x) Read It Watch It Talk to a Tutor Type here to search

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-12 points SCalcET8 3.4.063 A table of values for f, g, f, and g' is given. xf(x) g(x) f'(x) g'(x) 2 4 6 7 9 2 3 2 (a) If h(x)=rg(x), find h'(3). h'(3) (b) If H(x) g(f(x), find H'(2). H(2) Need Help? Read It WatehTak to a Tutor Talk to a Tutor Submit Assignme

Write the composite function in the form Ag(x)). [Identify the inner function u = g(x) and the outer function y = ru).] 3 (g(x), f(u)) = ( | 277

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