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Writing a Limit as a Definite Integral In Exercises 11 and $12,$ write the limit as a definite integral on the given interval, where $c_{i}$ is any point in the ith subinterval. \begin{equation} {\quad\quad \text { Limit }} \quad\quad\quad\quad\quad\quad\quad\quad {\text { Interval }} \\ \lim _{\|\Delta\| \rightarrow 0} \sum_{i=1}^{n}\left(3 c_{i}+10\right) \Delta x_{i} \quad[-1,5] \end{equation}

Name: Problem 11, Chapter 4: Calculus of a Single Variable
Uploaded: 2020-03-15T03:47:57-08:00
Duration: 2 min 48 s
Channel: Yaw Asomani
Description: Writing a Limit as a Definite Integral In Exercises 11 and 12, write the limit as a definite integral on the given interval, where ci is any point in the ith subinterval. Limit Interval limΔ→ 0∑i=1^n(3 ci+10) Δ xi [-1,5]

   Writing a Limit as a Definite Integral In Exercises 11 and $12,$ write the limit as a definite integral on the given interval, where $c_{i}$ is any point in the ith subinterval.
\begin{equation}
{\quad\quad \text { Limit }} \quad\quad\quad\quad\quad\quad\quad\quad {\text { Interval }} \\ \lim _{\|\Delta\| \rightarrow 0} \sum_{i=1}^{n}\left(3 c_{i}+10\right) \Delta x_{i} \quad[-1,5]
\end{equation}

Calculus of a Single Variable

Ron Larson 11th Edition

Chapter 4, Problem 11

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Solved by Expert Yaw Asomani

03/15/2020

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In this case, it is $3c_i + 10$. Show more…

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Writing a Limit as a Definite Integral In Exercises 11 and $12,$ write the limit as a definite integral on the given interval, where $c_{i}$ is any point in the ith subinterval. \begin{equation} {\quad\quad \text { Limit }} \quad\quad\quad\quad\quad\quad\quad\quad {\text { Interval }} \\ \lim _{\|\Delta\| \rightarrow 0} \sum_{i=1}^{n}\left(3 c_{i}+10\right) \Delta x_{i} \quad[-1,5] \end{equation}

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Key Concepts

Limit Process

The limit process in the context of Riemann sums is the procedure of letting the maximum width of the subintervals tend to zero, which ensures that the approximation of the area under the curve by the sum becomes exact. This process is fundamental in transitioning from the summation of finite slices to the continuous framework of integration.

Definite Integral

A definite integral represents the exact accumulation of quantities, such as area under a curve, over a given interval. It is defined as the limit of a Riemann sum as the norm of the partition (the maximum subinterval width) approaches zero.

Riemann Sum

A Riemann sum approximates the area under a curve by dividing the region into subintervals, calculating the value of the function at a chosen point within each subinterval, and summing the products of these function values with the subinterval widths. This process leads to approximating definite integrals over a specified interval.

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