Integral Calculus18. Evaluate the limit by recognizing it as a definite integral and then evaluating it.2л37limn- 4n(sec" ()+ sec?.4n| + .…· + sec?4n.+ sec?19. Find f,(5 – x*) dx using the limit definition.20. If V'(t) is the rate at which water is being pumped into the swimming pool at time t inminutes, what does S v'(t)dt represent?21. Differentiate the function below:sinxg(x) =t cost dt22. Evaluate the following integrals:tan-a) Sdxx*+4b) dxa) S×²VT= x dx23. The graph shown below represent a toy car's velocity where y is in feet per second andx represent time in second. Use the graph to estimate how far the toy car traveledbefore it came to a stop.108412.342.

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Answered: Integral Calculus 18. Evaluate the…

Integral Calculus 18. Evaluate the limit by recognizing it as a definite integral and then evaluating it. (sec () + sec (4n 37 + *+ sec (4n. lim n- 4n + sec? 4n

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter1: Functions

Section1.2: Functions Given By Tables

Problem 32SBE: Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it...

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Concept explainers

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

Integral Calculus
18. Evaluate the limit by recognizing it as a definite integral and then evaluating it.
2л
37
lim
n- 4n
(sec" ()
+ sec?
.4n
| + .…· + sec?
4n.
+ sec?
19. Find f,(5 – x*) dx using the limit definition.
20. If V'(t) is the rate at which water is being pumped into the swimming pool at time t in
minutes, what does S v'(t)dt represent?
21. Differentiate the function below:
sinx
g(x) =
t cost dt
22. Evaluate the following integrals:
tan-
a) S
dx
x*+4
b) dx
a) S×²VT= x dx
23. The graph shown below represent a toy car's velocity where y is in feet per second and
x represent time in second. Use the graph to estimate how far the toy car traveled
before it came to a stop.
10
8
4
1
2.
3
4
2.

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