Lecture Twenty-Three Practice

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Practice problems for Lecture Twenty Three Content

For each of the following functions use Riemann Sums to approximate the area under the graphs for the given intervals and values of $n$ .

1 : For the function $f(x) = x^2+1$ on the interval $[0,2]$ and using $n = 4$ calculate the:

Left endpoint approximation $\answer {\PIAI }$
Midpoint approximation: $\answer {\PIAII }$
Right endpoint approximation $\answer {\PIAIII }$

2 : For the function $f(x) = 2x + 3$ on the interval $[-1,3]$ and using $n = 4$ calculate the:

Left endpoint approximation $\answer {\PIIAI }$
Midpoint approximation: $\answer {\PIIAII }$
Right endpoint approximation $\answer {\PIIAIII }$

3 : For the function $f(x) = x^2 +2x$ on the interval $[0,30]$ and using $n = 3$ calculate the:

Left endpoint approximation $\answer {\PIIIAI }$
Midpoint approximation: $\answer {\PIIIAII }$
Right endpoint approximation $\answer {\PIIIAIII }$

4 : For the function $f(x) = 3x - 6$ on the interval $[2,12]$ and using $n = 5$ calculate the:

Left endpoint approximation $\answer {\PIVAI }$
Midpoint approximation: $\answer {\PIVAII }$
Right endpoint approximation $\answer {\PIVAIII }$

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factorial	$\blue{[?]}!$
exp	${\blue{[?]}}^{\blue{[?]}}$
sub	${\blue{[?]}}_{\blue{[?]}}$
frac	$\dfrac{\blue{[?]}}{\blue{[?]}}$
int	$\displaystyle\int{\blue{[?]}}d\blue{[?]}$
defi	$\displaystyle\int_{\blue{[?]}}^{\blue{[?]}}\blue{[?]}d\blue{[?]}$
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sum	$\displaystyle\sum_{\blue{[?]}}^{\blue{[?]}}\blue{[?]}$
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mat	$\left(\begin{matrix} \blue{[?]} \end{matrix}\right)$
*	$\cdot$
infinity	$\infty$
arcsin	$\arcsin\left(\blue{[?]}\right)$
arccos	$\arccos\left(\blue{[?]}\right)$
arctan	$\arctan\left(\blue{[?]}\right)$
sin	$\sin\left(\blue{[?]}\right)$
cos	$\cos\left(\blue{[?]}\right)$
tan	$\tan\left(\blue{[?]}\right)$
sec	$\sec\left(\blue{[?]}\right)$
csc	$\csc\left(\blue{[?]}\right)$
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mu	$\mu$
nu	$\nu$
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phi	$\phi$
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psi	$\psi$
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Gamma	$\Gamma$
Delta	$\Delta$
Theta	$\Theta$
Lambda	$\Lambda$
Xi	$\Xi$
Pi	$\Pi$
Sigma	$\Sigma$
Phi	$\Phi$
Psi	$\Psi$
Omega	$\Omega$

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