微積分
極限、導関数、最適化、関数挙動。
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calculator allowed let ( f(x)=sqrt{x} ). if the rate of change of ( f )…
A. \(\frac{1}{4}\)
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find the limit. (if the limit is infinite, enter ∞ or -∞, as appropriat…
\(1\)
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find the limit. (if the limit is infinite, enter ∞ or -∞, as appropriat…
\(0\)
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find the limit. (if the limit is infinite, enter ∞ or -∞, as appropriat…
\(\frac{9}{2}\)
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4. if the derivative of $f$ is given by $f(x)=e^{x}-3x^{2}$, at which o…
D. \(0.95\)
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in the diagram above, imagine an officer noting the time in which an in…
(a) \((-1,1)\) and \((3,-39)\) (b) \(-10\) (c) \(1.67\) (d) in the open interval \((a,b)\)
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at 2:00 p.m, a cars speedometer reads 30 mi/h. at 2:20 p.m. it reads 50…
\(\frac{v(\frac{1}{3})-v(0)}{\frac{1}{3}-0}=60\), \(0\lt c\lt\frac{1}{3}\), \(v^{\prime}(c) = 60\)
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6. - / 2 points details my notes ask your teacher suppose that ( 3 leq …
\(15\leq f(8)-f(3)\leq25\)
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if ( f(4)=3 ) and ( f^{prime}(x) geq 3 ) for ( 4 leq x leq 9 ), how sma…
\(18\)
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let ( f(x)=(x - 3)^{-2} ). find all values of ( c ) in ( (1,7) ) such t…
\(c=\text{DNE}\) For the conclusion: This does not contradict the Mean Value Theorem since \(f\) is not continuous at \(x = 3\).
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find the number c that satisfies the conclusion of the mean value theor…
\(1\)
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consider the following function. $f(x)=4 - x^{2/3}$ find $f(-8)$ and $f…
\( f(-8)=0 \) \( f(8)=0 \) \( c=\text{DNE} \) The correct option is: This does not contradict Rolle's Theorem, since \( f'(0) \) does not exist, and so \( f \) is not differentiab…
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find \\( \\frac { d y } { d x } \\) for \\( y = \\frac { \\sec x } { 1 …
\(\frac{\sec x\tan x}{(1 + \sec x)^{2}}\)
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mock exam for 2025 - 2026 - 1 1. calculate the definite integrals by re…
(1) \(-2.33\) (2) \(2.71\) (3) \(5.63\)
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1. let ( f ) be a differentiable function such that ( f(3)=2 ) and ( f^…
C. \(2.6\)
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find \\( \\frac{d p}{d q} \\) for \\( p=\\frac{\\cos q+\\sin q}{\\cos q…
\(\sec^{2}q\)
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find \\( \\frac { d r } { d \\theta } \\). \\( r = ( 7 + \\sec \\theta …
\(\sec^{2}\theta + 7\cos\theta\)
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find \\( \\frac { d r } { d \\theta } \\). \\( r = 1 - \\theta ^ { 4 } …
\(-\theta^{3}(4\sin\theta+\theta\cos\theta)\)
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find \\( \\frac { d s } { d t } \\). \\( s = 3 \\cot t - e ^ { - t } \\…
\(\frac{ds}{dt}=-3\csc^{2}t + e^{-t}\)
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answer: \\frac{\\sqrt{2}+5}{2} # ____ f(x)=\\frac{1}{x} f(e)=-3 to adva…
\(0\)
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homework7: problem 5 (2 points) find \\( \\frac{d y}{d x} \\) by implic…
\(\frac{y^{3}-9x^{2}-2xy}{x^{2}-3xy^{2}}\)
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find $\\frac{dy}{dx}$ for $y = 6x^{2}\\sin x + 12x\\cos x - 12\\sin x$.…
\(6x^{2}\cos x\)
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find $\\frac{dy}{dx}$ for $y = \\frac{\\csc x}{1 + \\csc x}$. $\\frac{d…
\(\frac{-\csc x\cot x}{(1 + \csc x)^{2}}\)
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homework7: problem 3 (2 points) for the equation given below, evaluate …
\(-\frac{4}{5}\)
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homework7: problem 2 (2 points) for the equation given below, evaluate …
\(-\frac{6}{95}\)
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homework7: problem 1 (2 points) for the equation given below, evaluate …
\(-\frac{2}{11}\)
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find \\( \\frac { d y } { d x } \\). \\( y = 2 \\sec x \\tan x \\) \\( …
\(2\sec^{3}x + 2\sec x\tan^{2}x\)
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use the formula ( f^{prime}(x)=lim _{z ightarrow x} \frac{f(z)-f(x)}{z …
\(\frac{7}{(x + 1)^{2}}\)
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find \\( \\frac { d y } { d x } \\) for \\( y = - 7 x + 3 \\cos x \\). …
\(-7-3\sin x\)
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3.) (6pts) suppose that ( f ) is a function with domain ( (-infty, inft…
\(\lim_{x ightarrow2}f(x)=7\)
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find the derivative of the given function. y = x² sin³x + x cos⁻⁵x \\fr…
$$2x\sin^{3}x+3x^{2}\sin^{2}x\cos x+\cos^{-5}x + 5x\cos^{-6}x\sin x$$
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find the derivative of the function ( y = (csc x - cot x)^{-1} ). ( \fr…
\(-\csc^{2}x-\csc x\cot x\)
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g(x)=\\frac{1}{2\\sqrt{x}} g(25)=2 to advance in the circuit, locate g(…
\(2\sqrt{2}-3\)
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find the derivative of the function ( y = sqrt{2 - 5x} ). ( \frac{dy}{d…
\(-\frac{5}{2\sqrt{2 - 5x}}\)
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write the function in the form ( y = f(u) ) and ( u = g(x) ). then find…
C. \(y = e^{u},u=-8x\) and \(\frac{dy}{dx}=-8e^{-8x}\)
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find the value or values of c that satisfy the equation \\( \\frac { f …
\(\frac{9}{2}\)
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write the function below in the form ( y = f(u) ) and ( u = g(x) ), the…
A. \(f(u)=u^{5}\), \(g(x)=5x - 12\) and \(\frac{dy}{dx}=25(5x - 12)^{4}\)
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given ( y = f(u) ) and ( u = g(x) ), find ( \frac{dy}{dx}=f(g(x))g(x) )…
\(4\cos(4x - 3)\)
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# 9 $f(x)=\\frac {2}{1+x^{2}}$ $f(-1)=3$. to advance in the circuit, lo…
\(f(\sqrt{3})=\frac{7\pi}{6}+3\)
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find the value or values of c that satisfy the equation \\( \\frac { f …
\(\frac{343\sqrt{7}}{2187}\)
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find equations of all lines having slope - 3 that are tangent to the cu…
A. There are two lines tangent to the curve with a slope of \(-3\). The equation of the line with the larger \(y\) - intercept is \(y=-3x + 27\) and the equation of the line with …
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show that the function $f(t)=\\sqrt{t}+\\sqrt{1 + t}-4$ has exactly one…
B. No
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answer: # 8 $y = csc x cot x, y(\frac{pi}{2}) = 6$ to advance in the ci…
\(9\)
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find equations of all lines having slope - 3 that are tangent to the cu…
A. The equation of the line with the larger \(y\) - intercept is \(y=-3x + 27\) and the other is \(y=-3x+3\)
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show that the function ( f(t)=sqrt{t}+sqrt{1 + t}-4 ) has exactly one z…
\(f^\prime(t)=\frac{1}{2\sqrt{t}}+\frac{1}{2\sqrt{1 + t}}\)
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find the slope of the following curve at ( x = 7 ). ( y=\frac{1}{x - 4}…
\(-\frac{1}{9}\)
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find the slope of the curve ( y = - 7 x ^ { 2 } ) at ( ( - 4, - 112 ) )…
\(56\)
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show that the function ( f(t)=sqrt{t}+sqrt{1 + t}-4 ) has exactly one z…
Since \(f(t)\) is continuous on \((0,\infty)\), \(f(0)<0\), \(f(t) ightarrow\infty\) as \(t ightarrow\infty\) (by Intermediate Value Theorem, there is at least one zero) and \(f^\…
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homework6: problem 4 (3 points) a potter forms a piece of clay into a r…
\(-\frac{1}{6}\text{ cm/s}\)
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find the slope of the functions graph at the given point. then find an …
\(\frac{7}{12}\)
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show that the function ( f(t)=sqrt{t}+sqrt{1 + t}-4 ) has exactly one z…
Since \(f(t)\) is continuous on \((0,\infty)\), \(f(0)<0\), \(\lim_{t ightarrow\infty}f(t)=\infty\) (so there is at least one zero by the Intermediate Value Theorem) and \(f(t)\) …
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the equation of the line tangent to the graph of $f(x)=\\sqrt{10x}$ at …
\(y=\frac{1}{2}x + 5\)
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homework6: problem 3 (3 points) water is leaking out of an inverted con…
\(0.178\)
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the slope of the graph of the function $f(x)=sqrt{10x}$ at $(10,10)$ is…
\(\frac{1}{2}\)
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which limit below is equal to the slope m of the curve at the given poi…
A. \(\lim_{h ightarrow0}\frac{\sqrt{10(10 + h)}-\sqrt{10\times10}}{h}\)
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homework6: problem 2 (3 points) a kite 100ft above the ground moves hor…
\(\frac{6}{625}\) radians per second.
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find the slope of the functions graph at the given point. then find an …
The slope \(m = - 10\) and the equation of the tangent line is \(y=-10x - 24\)
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homework6: problem 1 (3 points) a spherical balloon is to be deflated s…
\(-2548\pi\approx - 8007.26\) \(cm^{3}/min\). The rate at which air is removed is \(2548\pi\approx8007.26\) \(cm^{3}/min\) (we take the magnitude since rate of removal is a positi…
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find the slope of the functions graph at the given point. then find an …
The slope \(m = 27\) and the equation of the tangent line is \(y = 27x + 109\).
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hygiene for health creating connections social studies: world history i…
B. To demonstrate how good personal hygiene can limit the spread of diseases and increase health
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show that the function ( f(x)=x^{4}+5x + 3 ) has exactly one zero in th…
For "Can the derivative of \(f(x)\) be zero in the interval \([-1,0]\)": No. For "According to Rolle's Theorem, can there be another point \(x = b\) in this interval where \(f(a)=…
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use an identity to write the expression as a single trigonometric funct…
$\cos9x$
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simplify the expression. \\frac{1 - \\cos 52.74^{\\circ}}{\\sin 52.74^{…
\(26.37\)
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simplify the expression. \\frac{1 - \\cos 58.72^{\\circ}}{\\sin 58.72^{…
\(29.36\)
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f(0)=3 (simplify your answer.) according to the intermediate value theo…
B. No
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directions: for each of the following 7. ( f ( x ) = \frac { ( x + 2 ) …
The vertical asymptote is \(x = 3\), \(\lim_{x\to3^{-}}f(x)=\infty\), \(\lim_{x\to3^{+}}f(x)=-\infty\)
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show that the function ( f(x)=x^{4}+5x + 3 ) has exactly one zero in th…
\(4x^{3}+5\)
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show that the function ( f(x)=x^{4}+5x + 3 ) has exactly one zero in th…
The function \(f(x)=x^{4}+5x + 3\) has exactly one zero in the interval \([-1,0]\) because: 1. By the Intermediate Value Theorem (since \(f(-1)=-1\), \(f(0)=3\) and \(f(x)\) is co…
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which theorem can be used to determine whether a function f(x) has any …
\( 3 \)
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show that the function ( f(x)=x^{4}+5x + 3 ) has exactly one zero in th…
\( f(-1)=-1 \)
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show that the function ( f(x)=x^{4}+5x + 3 ) has exactly one zero in th…
A. Intermediate value theorem
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determine whether rolles theorem applies to the given function on the g…
A. Rolle's Theorem applies, and the point(s) it guarantees to exist is/are \(c = 1-\frac{3\sqrt{2}}{2}\)
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use identities to find values of the sine and cosine functions for the …
\(\cos\theta=\frac{\sqrt{26}}{26}\)
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# 4 $h(t)=t^{2}-t + 1$, $h(0)=-\\frac{1}{2}$ to advance in the circuit,…
\( h(1)=\frac{1}{3} \)
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which narrative point of view is shown in the passage? elizabeth looked…
third person limited
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which narrative point of view is shown in the passage? pa and vernon ar…
first person
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using the definition, calculate the derivative of the function. then fi…
\(f^{\prime}(x)=-2x\), \(f^{\prime}(-6) = 12\), \(f^{\prime}(0)=0\), \(f^{\prime}(5)=-10\)
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determine whether rolles theorem applies to the given function on the g…
Since \(f\) is not continuous on the closed interval \([\frac{\pi}{4},\frac{3\pi}{4}]\), not differentiable on the open interval \((\frac{\pi}{4},\frac{3\pi}{4})\) and \(f(\frac{\…
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which narrative point of view is shown in the passage? the door opened,…
first person
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7 multiple choice 10 points which concept can help toddlers to cope wit…
7. transitional object 8. communication difficulty 9. These methods focus on early detection in young children of delays and/or disabilities. 10. Authoritarian parenting is utiliz…
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question 5 0.5 pts which of the following segmentation is noted as impo…
Geographic
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3.6 the chain rule - ds3: problem 1 (6 points) let $f(x)=(x^{3}+4x + 2)…
\(f^\prime(x)=4(x^{3}+4x + 2)^{3}(3x^{2}+4)\) \(f^\prime(2)=373248\)
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3.4 derivatives as rates of change - da1: problem 14 (1 point) results …
\(8\) cubic mm/mm
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ling must spend no more than $40.00 on decorations for a party. she has…
She can buy from 0 to 12 bags, but no more.
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which explains why supreme court justices are given lifetime appointmen…
They protect justices from political pressure.
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hamilton on the courts role limited government can be preserved in prac…
Courts preserve limited government by protecting the Constitution from attack.
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the judicial power of the united states the judicial power shall extend…
identify the jurisdiction of the federal courts.
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similar to the progressives, wilson supported raising tariffs in order …
establishing a graduated income tax.
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let h(x)=x² - 2x. (a) find the average rate of change from 5 to 7. (b) …
(a) The average rate of change from 5 to 7 is \( 10 \). (b) The equation of the secant line is \( y = 10x-35 \).
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use a graphing calculator and a system of equations to find the roots o…
\(-1.95\), \(4.73\)
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1) evaluate the integral $\\int \\frac{\\sec^{2}t\\mathrm{d}t}{(\\tan t…
$\frac{1}{1-\tan t}+C$
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write the equation of a sine function with amplitude = 8 and period = 4…
B. There are two equations; the equation when \(A < 0\) is \(y=-8\sin(\frac{1}{2}x)\) and the equation when \(A>0\) is \(y = 8\sin(\frac{1}{2}x)\)
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use the graph to determine (a) open intervals on which the function is …
\((1,2),(4,5)\)
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the average rate of change from x = 0 to x = 15 is about -4.667. how do…
greater than
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find the amplitude (if one exists), period, and phase shift of the func…
The amplitude is \(4\). The period is \(2\). The phase shift is \(-\frac{1}{\pi}\).
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the function ( y = f(x) ) is graphed below. what is the average rate of…
\(-4\)
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place(s) limitations on congress when it comes to the rights of the cit…
A. The Bill of Rights
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3. calculate the definite integrals by referring to the following figur…
(1) \(1.408\) (2) \(-1.067\) (3) \(5.333\) (4) \(3.541\)
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which narrative point of view is shown in the passage? there is a brief…
second person
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a general limitation on the power of the president is the possibility o…
the possibility of impeachment.