Activity 8.5.2. Use known Taylor series and substitution and algebraic techniques to find a Taylor series representation for each of the following functions. In addition, state the interval of \(x\)-values for which you expect each Taylor series to converge.🔗 (a) \(g(x) = x^3 \sin(x^2)\)🔗 🔗(b) \(h(x) = e^{-x^4}\)🔗 🔗(c) \(p(x) = \dfrac{1}{1+5x}\)🔗 🔗(d) \(q(x) = x^2\ln(1+x^4)\)🔗 🔗(e) \(r(x) = \dfrac{e^{3x}-1}{3x}\)🔗 🔗🔗
