微积分
极限、导数、最优化与函数性质。
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the function ( f ) is given by ( f(x) = 3^x ). the function ( g ) is gi…
C. The graph of g is a combination of a vertical dilation of the graph of f and a reflection over the x - axis.
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1. the graph on the coordinate plane represents the given system. verif…
Since the ordered pair \((-2,6)\) satisfies both equations \(y=-2x + 2\) and \(y=\frac{1}{2}x+7\), it is a solution to the system of equations.
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the function ( f ) is given by ( f(x) = 2^x ), and the function ( g ) i…
B. A horizontal translation to the right 3 units
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let ( h(x) = f(x) cdot g(x) ), and ( k(x) = \frac{f(x)}{g(x)} ). use th…
A. $h'(-3)=4$ B. $k'(3)=\frac{1}{2}$
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the function ( f ) is given by ( f(x) = 2^x ), and the function ( g ) i…
B. A horizontal translation to the right 3 units
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write the quadratic function in standard form. $g(x) = x^2 - 8x$ $g(x) …
\(g(x)=(x - 4)^{2}-16\)
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evaluate the integral (int x^{7}(x^{8}-4)^{44}dx,) by making the approp…
$u = x^8 - 4$ $\frac{(x^8 - 4)^{45}}{360} + C$
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problem. 4 : the position function of a ball thrown into the air with a…
\(-105\)
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evaluate the integral \\(\\int \\frac{dx}{(6x + 10)^3}\\), by making th…
Appropriate substitution: $u = 6x + 10$ Integral result: $\boldsymbol{-\frac{1}{12(6x+10)^2} + C}$ (where $C$ is the constant of integration)
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7. 23×59.8 =
1375.4
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problem. 4 : the position function of a ball thrown into the air with a…
\( -16h - 105 \) ### Problem 5
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evaluate the indefinite integral.\\(\\int \\frac{2}{(t + 12)^8} dt\\)\\…
$-\frac{2}{7(t+12)^7}$
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problem. 1 : find the derivative of the function using the definition o…
\((-\infty, \infty)\)
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find the slope of the line passing through the pair of points or state …
(for slope part): A. The slope is \(-\frac{6}{5}\)
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evaluate the indefinite integral.\\(\\int x^3 \\sqrt{5 + x^4} dx\\)\\(\…
$\frac{1}{6}(5 + x^4)^{\frac{3}{2}}$
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problem. 1 : find the derivative of the function using the definition o…
The domain of the function \( f(x)=-6x - 9 \) in interval notation is \( (-\infty, \infty) \). So the first box should be filled with \( -\infty \) and the second box should be fi…
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problem. 1 : find the derivative of the function using the definition o…
\( -6 \) ### Problem 2
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find the slope of the line graphed below.
1
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exercises 1.5 substitution score: 100/170 answered: 10/17 question 14 e…
$\frac{9}{4}\sin^4 x + C$
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find the slope of the line graphed below.
$\frac{-5}{4}$
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question 2 the graph of a function $f(x)$ is shown below. graph of a fu…
To determine the graph of \( f'(x) \) from the graph of \( f(x) \), we analyze the **slope** (derivative) of \( f(x) \) at different points: ### Step 1: Analyze Intervals of Incre…
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question 1 the graph of a function \\( f(x) \\) is shown below: for how…
4
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the graph of a function $f(x)$ is shown below. which of the following c…
The second option (the graph with the wave - like curve symmetric about the origin, the one in the middle of the four options)
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find the slope of the line graphed below.
$\frac{3}{7}$
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question 3 suppose a particle moves along the ( x )-axis and that its p…
3 (corresponding to the option with value 3)
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the graph of a function $f(x)$ is shown below: for how many values of $…
4
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integrate \\(\\int_{-2}^{2} 21(3x + 2)^{6} dx\\) answer =
2113536
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complete the table and then graph the function. $y = \\frac{1}{3}x$ | x…
The completed table is: | \( x \) | \( y \) | | ---- | ---- | | 0 | 0 | | 3 | 1 | | 6 | 2 | | 9 | 3 | (For graphing, plot the points \((0,0)\), \((3,1)\), \((6,2)\), \((9,3)\) and…
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homework 12 (6.10) graphical analysis the graph of ( h(x) ) is defined …
1. $(-5, 2)$ 2. $x=2$ 3. $-4$ 4. $x=-2, 2, 5$ 5. $(-2, 5) \cup (5, 7)$ 6. $x=-2, 5$ 7. $(-5, -2)$ 8. $(-2, 2)$ 9. $(2, 7)$
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y = \\frac{1}{2}x + 4\ click to select points on the graph.
The y - values in the table (6 for x = 4, 7 for x = 6, 9 for x = 10) are correct according to the equation \( y=\frac{1}{2}x + 4 \).
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complete the table and then graph the function. $y = 2x$ | x | y | |---…
The completed table has points \((0,0)\), \((2,4)\), \((5,10)\). To graph the function, plot these points and draw a line through them.
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verify that ( y = sin 2t + 3cos 2t ) is a solution to the initial value…
\( 2\cos 2t - 6\sin 2t \)
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1. **find the relative extrema of $f(x) = x^3 + 3x^2 - 9x + 5$**
Relative maximum at $x=-3$ with value $32$; relative minimum at $x=1$ with value $0$
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function operations for use with exploration 5.5 essential question how…
(to the Essential Question): To sketch the graph of an arithmetic combination (sum, difference, product, or quotient) of two functions \( f(x) \) and \( g(x) \) using their graphs…
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Question was provided via image upload.
When \( x = 0 \), \( y = 0 \); when \( x = 4 \), \( y = 2 \); when \( x = 10 \), \( y = 5 \)
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consider the indefinite integral \\(\\int x^4 \\cdot \\sqrt2{x^5 - 8} \…
$u = x^5 - 8$ $du = 5x^4$ $\int \frac{1}{5}u^{\frac{1}{2}}$
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y = -4x + 13 x | y 1 | 2 | 3 | click to select points on the graph.
For \( x = 1 \), \( y = 9 \); for \( x = 2 \), \( y = 5 \); for \( x = 3 \), \( y = 1 \)
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4 sketch the graph of each line: $y = -\frac{3}{2}x - 1$
The graph of the line \(y =-\frac{3}{2}x - 1\) is drawn by first plotting the y - intercept \((0,-1)\) and then using the slope \(-\frac{3}{2}\) to find additional points (such as…
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1.1: order of operations score: 5/14 answered: 5/14 question 6 evaluate…
47
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1.1: order of operations score: 4/14 answered: 4/14 question 5 use the …
$(2+3)^2 = 25$ $2^2+3^2 = 13$
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1.1: order of operations score: 3/14 answered: 3/14 question 4 use the …
270
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exercises 1.5 substitution score: 50/170 answered: 5/17 question 6 eval…
$\frac{4}{7}\sin^7(x)$
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question 5 evaluate the integral by making the given substitution. \\(\…
$\frac{1}{4}\sec(4x)$
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exercises 1.5 substitution score: 30/170 answered: 3/17 question 4 eval…
$\frac{(x^6 - 1)^{14}}{84}$
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exercises 1.5 substitution score: 20/170 answered: 2/17 question 3 eval…
$\frac{(x^2+4x+9)^6}{6} + C$
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exercises 1.5 substitution score: 0/170 answered: 0/17 question 1 textb…
True
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20 graph the equation: $y = 2x + 3$
The graph of \( y = 2x + 3 \) is a straight line with a y - intercept at \( (0,3) \) and a slope of 2, passing through points like \( (1,5) \) and \( (-1,1) \) (and others found u…
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fill in the missing number. \\(\frac{4}{5} \times \frac{1}{2} = \frac{2…
5
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a. the free enterprise system is the best economic system because it al…
Producers can decide to make new or better products to attract consumers in the free enterprise system.
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17 graph the equation: $y = -\frac{1}{3}x - 4$
To graph \(y =-\frac{1}{3}x-4\): 1. Plot the y - intercept \((0, - 4)\). 2. Use the slope \(-\frac{1}{3}\) to find another point (e.g., from \((0,-4)\), move down 1 and right 3 to…
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match each equation with the sketch of its graph.
To solve this, we analyze each graph's key features (domain, range, starting point, direction) and match with the equation's properties. However, since the equations aren't provid…
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use technology to find points and then graph the function $y = 2^{x + 1…
The points with integer coordinates are \( (-1, -7) \), \( (0, -6) \), \( (1, -4) \), \( (2, 0) \), \( (3, 8) \) (and more can be calculated, e.g., \( x = 4 \) gives \( y = 2^{5}-…
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write the slope intercept form of the equation of the line. equation: $…
\(y =-\frac{1}{2}x-1\)
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use technology to find points and then graph the function $y = 2^x - 7$…
Five points with integer coordinates for \( y = 2^x - 7 \) are (0, -6), (1, -5), (2, -3), (3, 1), (4, 9). Plot these points and draw the exponential curve.
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use technology to find points and then graph the function ( y = 2^x - 7…
The graph is drawn by plotting the points \((-3,-6.875)\), \((-2,-6.75)\), \((-1,-6.5)\), \((0, - 6)\), \((1,-5)\), \((2,-3)\), \((3,1)\) and connecting them with a smooth curve, …
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find an explicit formula, f(n), for the following geometric sequence: 2…
$f(n) = 2 \cdot (-3)^{n-1}$
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multiply. 0.07 × 8
0.56
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multiply. 2 × 0.24
0.48
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solve the system of equations. y = -3x + 2 y = 2 - 3x y = mx + b m: slo…
### Part 1: Solve the system of equations The system of equations is: \[ \begin{cases} y = -3x + 2 \\ y = 2 - 3x \end{cases} \] #### Step 1: Analyze the equations Notice that both…
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of the function ( f(x) = 2x^2 + bx + c ) is shown. what are the values …
$b=-4$, $c=-6$
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solve the system of equations. $y = -3x + 2$ $y = 2 - 3x$ $y = mx + b$ …
- For the equation \( y=-3x + 2 \): - Slope (\( m \)): \(-3\) - y - intercept (\( b \)): \(2\) - To graph: Plot \( (0,2) \), use slope \( \frac{-3}{1} \) to find other points (e.g…
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the axis of symmetry for the function $f(x) = -2x^2 + 4x + 1$ is the li…
B. (1, 3)
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over what interval is the function shown in the table increasing? $f(x)…
B. $x<0$
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7. lesson quiz for which function is the average rate of change over th…
D. $k(x)=2x^2$
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calculate. (1) $\frac{5}{6} - \frac{3}{4} = $ (2) $\frac{2}{3} - \frac{…
$\frac{1}{12}$ ### (2)
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adam graphs ( f(x) = x^2 ) and ( g(x) = 3x^2 ). which of the following …
C. y-value when x = 5
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express the function graphed on the axes below as a piecewise function.…
\(f(x)=\begin{cases}6x, & x\leq1\\x + 4, & x>4\end{cases}\)
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fill in the equation for this function. y = ?(x - )^3 +
\( y = -2(x - 3)^3 + 3 \)
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evaluate the expression. \\(\frac{3}{4} - \frac{1}{4} \times \frac{1}{2…
\(\frac{5}{8}\)
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graph the function ( h(x) = 2x - 5 ).
# Explanation: ## Step1: Identify the function type The function \( h(x) = 2x - 5 \) is a linear function in the form \( y = mx + b \), where \( m = 2 \) (slope) and \( b = -5 \) …
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evaluate the function graphically. find ( f(1) )
$-8$
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evaluate the indefinite integral.\\(\\int x^4 \\sqrt{14 + x^5} dx\\)\\(…
$\frac{2}{15}(14 + x^5)^{\frac{3}{2}}$
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evaluate each expression. 5. \\(\frac{(-14 \times 0.5)^3}{14}\\)
$-\frac{49}{2}$ or $-24.5$
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evaluate the indefinite integral.\\(int x^{8}e^{x^{9}}dx\\)\\(\\boxed{}…
$\frac{1}{9}e^{x^9}$
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evaluate the function graphically. find $f(-1)$
$2$
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find $f^{-1}(-8)$.\ \ | $x$ | $f(x)$ |\ | --- | --- |\ | $-4$ | $6$ |\ …
15
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a car enthusiast learns that a particular model of car, which costs $34…
\(\$6124.42\)
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suppose that the future price p(t) of a certain item is given by the fo…
200 ### Part 2: Growth or Decay
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5. evaluate the logarithm. \\(\\log_{10} 0.001 = \\square\\)
\(-3\)
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solve $3^x = 7$. round your answer to the nearest thousandth. $x\\appro…
$x \approx 1.771$
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greg is in a car at the top of a roller - coaster ride. the distance, (…
\( 0 < t < 3 \) (the option corresponding to this interval)
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domain and range matching match the domain and range cards with the gra…
To solve the domain and range matching for the given graphs, we analyze each graph's horizontal (domain) and vertical (range) extent: ### 1. First Graph (Top - Left) - **Domain**:…
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express \\(\\frac{5}{6}\\) as a decimal. select one answer a 0.83 b \\(…
B. $0.\overline{83}$
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6. short answer for the equation y = 2x - 5, explain how the graph move…
Starting from any point on the graph of $y=2x-5$, for each 1-unit horizontal shift right, the graph shifts 2 units up; for each 1-unit horizontal shift left, the graph shifts 2 un…
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8. $y = -4 + \\frac{6}{5}x$
The line passes through points (0, -4) and (5, 2), and extends infinitely in both directions.
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determine the end behavior of the graph of the given polynomial functio…
down and up
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15. what is the value of $24\\div4+(7 - 3)-2\\cdot4 + 6^2$?
64
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click to select points on the graph.
\(\frac{1}{3}\) (Note: If the actual question was different, like y-intercept, for green line y-intercept is 6 (at x=0), blue is 5. Adjust based on the actual question, but since …
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13. what is the value of $2(4)+6cdot2 - 16div4 + 52$?
68
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when yoshi graphed the lines $y = 2x + 3$ and $y = 2x - 2$, she got the…
a. Line $b$ matches $y=2x+3$; Line $a$ matches $y=2x-2$ b. The line $y=2x+1$ will lie between lines $a$ and $b$. It is parallel to the other two lines (same slope $2$) and has a y…
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2)16 8)48 6)60 10)50 3)27 6)18
8, 9, 5, 8, 6, 10, 5, 9, 3
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the court case schenck v. united states focused on whether or not the g…
C. speech. ### Question 11 (Charles Schenck's accusation)
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solve the following system of equations graphically on the set of axes …
The solution is \( x = 1 \), \( y=-5 \) (or the point \( (1, -5) \)).
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7)28 6)30 9)45 5)20 6)48 4)20 7)56 2)10 2)16 8)48 6)60 8)64 10)50 3)27 …
4, 5, 5, 4 8, 5, 8, 5 8, 6, 10, 8 5, 9, 3, 9
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4)32 6)48 4)20 9)54 2)16 8)48 7)63 10)50 3)27
1. $8$ 2. $8$ 3. $5$ 4. $6$ 5. $8$ 6. $6$ 7. $9$ 8. $5$ 9. $9$
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completar unlimited attempts left due february 3rd 11:59 pm completa la…
To solve this, we need to use the "se" construction (passive se or impersonal se) in the present indicative with the given verbs. Let's analyze each sentence: ### 1. ____ gritar (…
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number correct: \\(5\\enclose{longdiv}{15}\\) \\(10\\enclose{longdiv}{7…
$3$, $7$, $6$, $10$, $7$, $8$
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the following system of equations graphically on the set of axes below.…
1. For $y=-2x-4$, plot the points $(0, -4)$ and $(-2, 0)$, then draw a line through them. 2. For $y=x-7$, plot the points $(0, -7)$ and $(7, 0)$, then draw a line through them. 3.…
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i peered out the window, whispering a quiet plea. please, please, pleas…
A. The author uses first-person point of view to help the reader understand what the experience felt like for the narrator.
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which sentence uses a third - person limited point of view? a. ian smil…
C. The flu shot felt like a beesting in Marco's right arm.