Calculus: An Applied Approach (MindTap Course List)
10th Edition
ISBN: 9781305860919
Author: Ron Larson
Publisher: Cengage Learning
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Chapter A2, Problem 3E
(a)
To determine
To calculate: The value of the expression
(b)
To determine
To calculate: The value of the expression
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Students have asked these similar questions
Given lim x-4 f (x) = 1,limx-49 (x) = 10, and lim→-4 h (x) = -7 use the limit properties
to find lim→-4
1
[2h (x) — h(x) + 7 f(x)] :
-
h(x)+7f(x)
3
O DNE
17. Suppose we know that the graph below is the graph of a solution to dy/dt = f(t).
(a) How much of the slope field can
you sketch from this information?
[Hint: Note that the differential
equation depends only on t.]
(b) What can you say about the solu-
tion with y(0) = 2? (For example,
can you sketch the graph of this so-
lution?)
y(0) = 1
y
AN
(b) Find the (instantaneous) rate of change of y at x = 5.
In the previous part, we found the average rate of change for several intervals of decreasing size starting at x = 5. The instantaneous rate of
change of fat x = 5 is the limit of the average rate of change over the interval [x, x + h] as h approaches 0. This is given by the derivative in the
following limit.
lim
h→0
-
f(x + h) − f(x)
h
The first step to find this limit is to compute f(x + h). Recall that this means replacing the input variable x with the expression x + h in the rule
defining f.
f(x + h) = (x + h)² - 5(x+ h)
=
2xh+h2_
x² + 2xh + h² 5✔
-
5
)x - 5h
Step 4
-
The second step for finding the derivative of fat x is to find the difference f(x + h) − f(x).
-
f(x + h) f(x) =
= (x²
x² + 2xh + h² -
])-
=
2x
+ h² - 5h
])x-5h) - (x² - 5x)
=
]) (2x + h - 5)
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Chapter A2 Solutions
Calculus: An Applied Approach (MindTap Course List)
Ch. A2 - Prob. 1CPCh. A2 - Prob. 2CPCh. A2 - Prob. 3CPCh. A2 - Prob. 4CPCh. A2 - Prob. 1ECh. A2 - Prob. 2ECh. A2 - Prob. 3ECh. A2 - Prob. 4ECh. A2 - Finding Distance on the Real Number Line In...Ch. A2 - Prob. 6E
Ch. A2 - Prob. 7ECh. A2 - Prob. 8ECh. A2 - Prob. 9ECh. A2 - Prob. 10ECh. A2 - Prob. 11ECh. A2 - Prob. 12ECh. A2 - Prob. 13ECh. A2 - Prob. 14ECh. A2 - Prob. 15ECh. A2 - Prob. 16ECh. A2 - Prob. 17ECh. A2 - Prob. 18ECh. A2 - Prob. 19ECh. A2 - Prob. 20ECh. A2 - Prob. 21ECh. A2 - Prob. 22ECh. A2 - Prob. 23ECh. A2 - Prob. 24ECh. A2 - Prob. 25ECh. A2 - Prob. 26ECh. A2 - Prob. 27ECh. A2 - Prob. 28ECh. A2 - Prob. 29ECh. A2 - Prob. 30ECh. A2 - Prob. 31ECh. A2 - Prob. 32ECh. A2 - Stock Price A stock market analyst predicts that...Ch. A2 - Prob. 34ECh. A2 - Prob. 35ECh. A2 - Prob. 36ECh. A2 - Prob. 37ECh. A2 - Prob. 38ECh. A2 - Prob. 39ECh. A2 - Prob. 40ECh. A2 - Quality Control In determining the reliability of...
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- Evaluate the integral using integration by parts. Sx² cos (9x) dxarrow_forwardLet f be defined as follows. y = f(x) = x² - 5x (a) Find the average rate of change of y with respect to x in the following intervals. from x = 4 to x = 5 from x = 4 to x = 4.5 from x = 4 to x = 4.1 (b) Find the (instantaneous) rate of change of y at x = 4. Need Help? Read It Master Itarrow_forwardVelocity of a Ball Thrown into the Air The position function of an object moving along a straight line is given by s = f(t). The average velocity of the object over the time interval [a, b] is the average rate of change of f over [a, b]; its (instantaneous) velocity at t = a is the rate of change of f at a. A ball is thrown straight up with an initial velocity of 128 ft/sec, so that its height (in feet) after t sec is given by s = f(t) = 128t - 16t². (a) What is the average velocity of the ball over the following time intervals? [3,4] [3, 3.5] [3, 3.1] ft/sec ft/sec ft/sec (b) What is the instantaneous velocity at time t = 3? ft/sec (c) What is the instantaneous velocity at time t = 7? ft/sec Is the ball rising or falling at this time? O rising falling (d) When will the ball hit the ground? t = sec Need Help? Read It Watch Itarrow_forward
- Find the slope of the tangent line to the graph of the function at the given point. f(x) = -4x + 5 at (-1, 9) m Determine an equation of the tangent line. y = Need Help? Read It Watch It SUBMIT ANSWERarrow_forwardFind the slope of the tangent line to the graph of the function at the given point. f(x) = 5x-4x² at (-1, -9) m Determine an equation of the tangent line. y = Need Help? Read It Master It SUBMIT ANSWERarrow_forwardFor what value of A and B the function f(x) will be continuous everywhere for the given definition?..arrow_forward
- 2. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.4.006.MI. Use the Table of Integrals to evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) 7y2 y² 11 dy Need Help? Read It Master It SUBMIT ANSWER 3. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.4.009. Use the Table of Integrals to evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) tan³(12/z) dz Need Help? Read It Watch It SUBMIT ANSWER 4. [-/1 Points] DETAILS MY NOTES SESSCALCET2 6.4.014. Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.) 5 sinб12x dx Need Help? Read Itarrow_forwardPlease refer belowarrow_forwardy"-9y+20y= 80t-156 y(0) = −6, y'(0) = 5 y(t) =arrow_forward
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