Express the limit as a deﬁnite integral.

-$ \lim_{||{\mathrm{P} \| \rightarrow 0}} \sum_{\mathrm{k}=1}^{\mathrm{n}} \frac{10}{\mathrm{c}_{\mathrm{k}}^{7}} \Delta \mathrm{x}_{\mathrm{k}} $where $\mathrm { P }$ is a partition of $[ 4,5 ]$
A) $\int _ { 4 } ^ { 5 } \frac { 10 } { x ^ { 7 } } d x$
B) $\int _ { 1 } ^ { n } \frac { 10 } { x } d x$
C) $\int _ { 4 } ^ { 5 } \frac { 10 } { x } d x$
D) $\int _ { 5 } ^ { 4 } \frac { 10 } { x ^ { 7 } } d x$

Question

Express the limit as a deﬁnite integral.

-$ \lim_{||{\mathrm{P} \| \rightarrow 0}} \sum_{\mathrm{k}=1}^{\mathrm{n}} \frac{10}{\mathrm{c}_{\mathrm{k}}^{7}} \Delta \mathrm{x}_{\mathrm{k}} $where $\mathrm { P }$ is a partition of $[ 4,5 ]$
A) $\int _ { 4 } ^ { 5 } \frac { 10 } { x ^ { 7 } } d x$
B) $\int _ { 1 } ^ { n } \frac { 10 } { x } d x$
C) $\int _ { 4 } ^ { 5 } \frac { 10 } { x } d x$
D) $\int _ { 5 } ^ { 4 } \frac { 10 } { x ^ { 7 } } d x$

Quizplus · Accepted Answer

By definition, the limit can be expressed as a definite integral as:

$$\lim_{||{\mathrm{P} \| \rightarrow 0}} \sum_{\mathrm{k}=1}^{\mathrm{n}} \frac{10}{\mathrm{c}_{\mathrm{k}}^{7}} \Delta \mathrm{x}_{\mathrm{k}} = \int_{4}^{5} \frac{10}{x^7} dx$$

Therefore, the best choice is (A).

Express the Limit as a Deﬁnite Integral lim⁡∣∣P∥→0∑k=1n10ck7Δxk \lim_{||{\mathrm{P} \| \rightarrow 0}} \sum_{\mathrm{k}=1}^{\mathrm{n}} \frac{10}{\mathrm{c}_{\mathrm{k}}^{7}} \Delta \mathrm{x}_{\mathrm{k}} lim∣∣P∥→0​∑k=1n​ck7​10​Δxk​

Express the Limit as a Deﬁnite Integral $\lim_{||{\mathrm{P} \| \rightarrow 0}} \sum_{\mathrm{k}=1}^{\mathrm{n}} \frac{10}{\mathrm{c}_{\mathrm{k}}^{7}} \Delta \mathrm{x}_{\mathrm{k}}$