Question

7. Use the limit definition to evaluate each improper integral. \begin{align} (a) \int_{-2}^{0} \frac{4}{\sqrt{(x+2)^{5}}} dx \\ (b) \int_{0}^{\infty} \frac{1}{e^{x} + e^{-x}} dx \text{ with the Given formula } \int \frac{1}{e^{x} + e^{-x}} dx = \arctan(e^{x}) + C. \end{align} 6. A sequence is defined by $a_1 = 1$, $a_n = \frac{1}{2}(a_{n-1} + 6)$ for $n \ge 2$. (1) Find $a_2$ and $a_3$. (2) Assume $\lim_{n \to \infty} a_n$ exists. Find $\lim_{n \to \infty} a_n$.

          7. Use the limit definition to evaluate each improper integral.
\begin{align*}
(a) \int_{-2}^{0} \frac{4}{\sqrt{(x+2)^{5}}} dx \\
(b) \int_{0}^{\infty} \frac{1}{e^{x} + e^{-x}} dx \text{ with the Given formula } \int \frac{1}{e^{x} + e^{-x}} dx = \arctan(e^{x}) + C.
\end{align*}
6. A sequence is defined by $a_1 = 1$, $a_n = \frac{1}{2}(a_{n-1} + 6)$ for $n \ge 2$.
(1) Find $a_2$ and $a_3$.
(2) Assume $\lim_{n \to \infty} a_n$ exists. Find $\lim_{n \to \infty} a_n$.

7. Use the limit definition to evaluate each improper integral.

(a) ∫-2^0(4)/(√((x+2)^5)) dx

(b) ∫0^∞(1)/(e^x + e^-x) dx with the Given formula ∫(1)/(e^x + e^-x) dx = arctan(e^x) + C.

6. A sequence is defined by a1 = 1, an = (1)/(2)(an-1 + 6) for n ≥ 2.
(1) Find a2 and a3.
(2) Assume limn →∞ an exists. Find limn →∞ an.

Added by Ines C.

Calculus

Ron Larson, Robert P. Hostetler, Bruce… 8th Edition

Chapter 4

Instant Answer

Solved by Expert Imogen Dell

Step 1

We need to find a₁₀ and a₁₁. Show more…

Show all steps

Thanks for your feedback!

Use the limit definition to evaluate each improper integral. 6. A sequence is defined by aâ‚ = 1, aâ‚™ = aâ‚™â‚‹â‚ + 6 for n â‰¥ 2. Find aâ‚â‚€ and aâ‚â‚. 2. Assume limâ‚™â†’c aâ‚™ exists. Find limâ‚™â†’c aâ‚™.