**is** **the** **radius** **of** **convergence** **of** **the** **Maclaurin** **series**. (a) Use the ratio test to find . R. (b) Write the first four nonzero terms of the **Maclaurin** **series** **for** . **f** ′, the derivative of . **f**. Express . **f** ′ as a ... <⇒ <**1** **The** **radius** **of** **convergence** **is** . **1**. 3. R = **1** : sets up ratio. Find the **radius** **of** **convergence** **of** **the** **Maclaurin** **series** **of** each function. Find the **Maclaurin** **series** **of** $\sinh x=\frac{e^{x} e^{-x}}{2}$. Answer. View Answer. Related Courses. Calculus 2 / BC. Calculus. Chapter 10. Power **Series**. Section 4. Working with Taylor **Series**. Related Topics. **Series**. Discussion. **The** five steps for determining the **Maclaurin** **Series** **of** f(x) = ln(1+x) are as follows. ... State the **radius** **of** **convergence**. **The** **Maclaurin** **series** **for** e^x is **1** + x + fraction {x^2}{2!} +fraction {x^3.

**Maclaurin**

**Series**

**Radius**

**of**Convergenceby integralCALC / Krista King. ← Video Lecture 165 of 50 → .

**1**: Area Under the Curve (Example

**1**) 2: Area Under the Graph vs. Area Enclosed by the Graph 3: Summation Notation: Finding the Sum 4: Summation Notation: Expanding 5: Summation Notation: Collapsing 6: Riemann Sums Right Endpoints 7: Riemann. Our first few terms are therefore.

**1**− 2x + 6x2 2 − 24x3 6. =

**1**− 2x +3x2 − 4x3. Which can be written as ∞ ∑ n=

**1**( −

**1**)n+

**1**(n)xn−

**1**. The

**radius**of converge is given by the ratio test. = lim n→∞ ( −

**1**)n+

**1**+

**1**(n +

**1**)xn+

**1**−

**1**( −

**1**)n+1n(xn−

**1**) = lim n→∞ ( −

**1**)n+2(n +

**1**)xn ( −

**1**)n+

**1**(n)xn−

**1**. = lim n→∞ ( −

**1**)

**1**n +

**1**n x. We know that the coefficient of the

**series**and your calls the ants order derivative of the function at zero over and sectorial and their sickles and plus one factorial over and factorial vehicles and platform enhance affects. He calls the song involved and from zero to infinity and plus one times X to the power of now they know that the

**radius**

**of**

**convergence**equals limits were and goes to.