Infinite Sequences and Series (BC Only)

$\left|\dfrac{(-1)^n\sin^{(n)}(c)}{(n+1)!}\left(\dfrac{\pi}{4}-\dfrac{\pi}{6}\right)^{n+1}\right|$ for some c between $\pi/4$ and $\pi/6$

$\left|\dfrac{f''(\pi/6)\left(\dfrac{\pi}{4}-\dfrac{\pi}{6}\right)^{2}}{2!}\right|$

$\left|\dfrac{(-1)^n\cos^{(n)}(c)}{(n)!}\left(\dfrac{\pi}{4}-\dfrac{\pi}{6}\right)^n\right|$ where n=3 and $\pi/6<c<\pi/4$

$\left|\dfrac{f^{(n+1)}(c)(\tanh(c))^{(n+1)}}{(n)!}\right|$ where n=2 and c is near zero

$x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + ...$

$x + \frac{x^3}{3!} + \frac{x^5}{5!} + \frac{x^7}{7!} + ...$

$x + x^2 + x^3 + x^4 + ...$

$x - x^2 + x^3 - x^4 + ...$

$1 + 2x + 2x^2 + \frac{4}{3}x^3$

$1 - 2x + 2x^2 - \frac{4}{3}x^3$

$1 - x - \frac{x^2}{2} - \frac{x^3}{6}$

$1 + x + \frac{x^2}{2} + \frac{x^3}{6}$

There is no such value for k.

$k=\frac{1}{4}$

$k=4$

$k=-4$

BETWEEN -5 AND +5 (-5 LOOK AT THE VALUE OF EXERCISES WORDING CALLED TO THE STANDARD EQUATION WHICH IS A MAVALURIN EXPANSION FOR EXPONENTIAL FUNCTIONS THAT ALWAYS CONVERGES FOR ALL REAL NUMBERS AS THE RADIUS OF CONVERGENCE IS INFINITE

ONLY NEGATIVE REAL NUMBERS ($-\infty < x < 0$)

All real numbers ($-\infty < x < \infty$)

Only positive real numbers ($0 < x < \infty$)

$\frac{1}{5!}$

$\frac{1}{3!}$

$\frac{1}{6!}$

$\frac{2}{5!}$

$\frac{5!}{4!}=5$

$\frac{5!}{5!}=1$

$\frac{(5!)^p}{(5-p)! \cdot p}$ where $p \neq 5$ are irrelevant terms.

$\frac{5!}{6!}=0$

Discarding non-dominant terms before integrating

Integration by partial fractions

Trigonometric substitution

Direct integration

Expanion will only Even Powered Terms

Exponsion won't include any powerds terms

Expanions will have both even and odd powered terms

Expanion will only have odd powered Terms

The first derivative, $f'(0)$

The limit of the function as $x$ approaches 0

$f(x)$ itself

The constant term, $f(0)$