Calculus Questions & Answers

The figure shows the graph of f. (b) Which of the cx-values A, B, C, D, E, F and G appear to be inflection points of f? 

4. (3.0pt) Calcule (a) \( \lim _{x \rightarrow 1} \frac{\ln (x)}{-x+1} \) (b) \( \lim _{x \rightarrow 0} \frac{e^{3 x}-1}{\sin x} \)

Un tanque metálico para almacenar sustancias quimicas debe tener la forma de un sólido de revolución generado al hacer girar alrededor del eje \( x \), la región comprendida entre este y la curva de la función \( y=\operatorname{sen} x \), entre \( 0 \leq x \leq \pi / 2 \), unido a un cilindro circular recto, con tapa en el extremo, de 1 pie de radio interior entre \( \pi / 2 \leq x \leq \pi \).

Evaluate the limit, if possible. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. ( A. \( \lim _{h \rightarrow 0} \frac{\sqrt{169+h}-13}{h}=\square \) (Type an exact answer.) B. The limit does not exist.

\( \int_{2}^{5} \frac{1}{x^{2}} d x ; n=9, w_{j} \) as \( d \) extremo derecho.

3) Sea \( F(x)=\frac{x^{3}+3 x-x^{2}-3}{5 x^{2}-5} \quad \) si \( x<1 \) HACLAR \( \lim _{x \rightarrow 1} F(x) \) y \( \lim _{x \rightarrow 0} F(x) \)

Let \( f(x)=\frac{10}{(x-6)^{2}} \). Estimate the limit \[ \lim _{x \rightarrow 6} f(x) \] by using the table approach: Left-sided:\( \begin{tabular}{|l|l|l|l|} \hline\( x \) & \( f(x) \) & \\ \hline 5.95 & 4000 & & (Round to nearest whole value.) \\ \hline 5.995 & 400000 & \( \sigma^{\circ} \) & (Round to nearest whole value.) \\ \hline 5.9995 & 40000000 & \( \sigma^{\infty} \) & (Round to nearest whole value.) \\ \hline 5.99995 & 4000000000 & \( \sigma^{\infty} \) & (Round to nearest whole value.) \\ \hline \end{tabular}\) Right-sided: Therefore \[ \lim _{x \rightarrow 6} f(x)= \] \( \square \)ANSWER ONLY LAST PART PLEASE

Exo1: Let the series \( \sum h_{n} \) such as, \( \forall n \in \mathbb{N}, \forall x \in \mathbb{R}_{+} ; h_{n}(x)=(-1)^{n} \frac{n}{n^{2}+x}: \) 1. Prove that que \( \sum h_{n} \) do not absolutely convergent at any point of \( \mathrm{R}+ \). 2. Prove that que \( \sum h_{n} \) converges uniformly on \( \mathrm{R}+ \) Voir: \( \underline{\text { Asanalyse 1-2-3 Guelma.pdf }} \) exo1 page 372

d) \( \lim _{x-1}\left(x^{5}-2 x-6\right) \)

\( \int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { 2 \pi n } 4 n - n ^ { 2 } 6 \)