Math
On the graph of the function f(x)=(1+x)^2 which of the following represents the slope of the secant line connecting the point on the graph with x-coordinate 1 and the the point on the graph with x-coordinate 1+h?
((2+h)^2−4)/h
On the graph of the function f(x) = (2 + x)^2 which of the following represents the slope of the secant line connecting the point on the graph with x-coordinate 1 and the the point on the graph with x-coordinate 1+h?
((3+h)^2−9)/h
The domain of the function f(x) = (|x+5|-2)/ square root x-3
(3,∞)
Suppose you charge $45/hr to tutor calculus and you work 10 hours a week. By raising your hourly rate you would lose business at a rate of 1 hour per $3 increase. Which expression below would you use to optimize your income using calculus? Here x stands for the number of dollars that the tutor increases the hourly rate.
(45+x)(10−x/3)
∫2..1 lnx/x dx.
(ln2)^2/2
If the position of an object is given by s(t) = 2 - t^2, then what is the average velocity of the object over the time interval 1≤t≤3?
-4
P(x, √5/3) is a point on the unit circle in the second quadrant, and θ is the angle whose terminal side passes through P. Find the value of tanθ
-√5/2
Suppose the second derivative of f is given to us in factored form by the following formula: f′′(x)=x^2(x+1)^5/(x-1)^4. How many inflection points does f have?
1
What expression estimates the integral ∫4..2 ln xdx using a Riemann sum with 4 rectangles and right endpoints?
1/2(ln(2.5)+ln(3)+ln(3.5)+ln(4))
Which of the following is equal to \displaystyle \ln\left(\sqrt{\frac{xy^2}{z^3}}\right)ln(z3xy2)?
21(lnx+2lny−3lnz)
Find the work done by a force F = √2x+1 N to move an object along a straight path from a distance of 0 meters to a distance of 4 meters.
26/3 J
Suppose the second derivative of ff is given to us in factored form by the following formula (x)=x^3(x−1)^2(x−2)(x+1)^3. How many inflection points does ff have?
3
Consider the function f (x) = - 2 x^5 + 13 x^4 -7x^3-3x^2. What is the smallest number n such that f^n (x) = 0 for all x ? (f(n) is the n-th derivative of f )
6
Suppose the function f is defined and continuous on a closed and bounded interval [a,b] and c is a point in the interior of [a,b]. Which of the following statements is true?
If f'(c)is undefined, then c is a critical point of f
The linear approximation to f(x) = tanx at a=4/π is
L(x)=2x+1−(π/2)
The linear approximation of f(x)=xsinx at a=2π is
L(x)=2π(x−2π).
The linear approximation of (x)=sin^2(x) at a=4π is
L(x)=x+1/2−4/π.
An object is moving along the xx-axis. The position of the object at time t is given by the function s(t)=−16t^2+64. Which of the following statements is correct?
The average speed of the object between t=0 and t=2 is 32.
Consider the piecewise function f(x) = x^2+2x-1, x < 0 x-1 , x⩾0.
The function ff is continuous at x=0x=0 because the left limit and right limit exist and are the same and equal to f(0)
lim -> x->π (1+tanx)/(1-cosx)
The limit equals 1/2 and can be found using direct substitution of x=π into the function.
Which of the following statements is FALSE about f(x) = e^x
The range of f is (−∞,∞)
An object is moving along the x-axis. The position of the object at time t is given by the function s(t)=−16t^2+64. Which of the following statements is correct?
The velocity of the object at t=2 is −64.
An object is moving along the x-axis. Let s(t), v(t) and a(t) be functions giving the position, the velocity and the acceleration of the object at time t. Which of the following statements is correct?
a(t)=s′′(t).
Find the absolute extrema of f(x)=x^2/4−√x on the interval [0,4]
absolute minimum: -3/4 absolute maximum: 2
Find the absolute extrema of f(x) = {x^4}/{4} - 2 sq root of {x} on the interval [0,4]
absolute minimum: -7/4, absolute maximum: 60
Consider the function f(x) = x^4 - 4x^3f(x)=x4−4x3. Which of the following is NOT true?
f has local extrema at x=0x=0 and x = 3x=3
Which statement is correct about the function f(x)=(x+1)/ sq root (x^2+1)
f has two horizontal asymptotes
Which of the following statements is true about a continuous function f defined on a closed and bounded interval I?
f must have both an absolute maximum and an absolute minimum on I
Let f be a continuous function such that f(0) = 5 and f'(0) = 2. Which of the following statements is correct?
f(0.1) is approximately 5.2.
Let f be a continuous function such that f(3.2) = 3 and f′(3)=5. Which of the following statements is correct?
f(3) is approximately 2.
Let ff be a continuous function such that f(0.1) = 5.2 f(0.1)=5.2. Which of the following statements is correct?
f′(0) is approximately 2.
Let f be a continuous function such that f(1.2) = 3 and f(1.2)=3. Which of the following statements is correct?
f′(1) is approximately 5.
Let f be a function and let c be a value inside the domain of f. Which of the following statements is correct?
f′(c), if exists, measures the instantaneous rate of change of f at x=c.
Let ff be a continuous function which is differentiable at c. Which of the following statements is correct?
f′(c)=h→0limhf(c+h)−f(c).
Let f be a continuous function which is differentiable at c. Which of the following statements is correct?
f′(c)≈f(c+h)−f(c)/h for small h
Stretch the graph of f(x) = x^2 vertically by a factor of 2 and reflect it about the y axis. What function do you get?
g(x)=2x^2
Shift the graph of (x)=3√x by one unit upward and two units to the right. What function do you get?
g(x)=3√x−2 +1
If g(x) = {x^2 f(x)}/{1 + 3x}, then which of the following is equal to g'(x)?
g′(x)=(1+3x)(x^2f′(x)+2xf(x))−3x2f(x))/(1+3x)^2
On the graph of the function f(x)=(2+x)^2 which of the following represents the slope of the tangent line to the graph at the point with x-coordinate 1?
lim h->0 ((3+h)^2−9)/h
Which of the following limits does not have an indeterminate form?
limx→0+ x^(x+1)
For which of the following limits can you use L'Hôpital's Rule directly?
lim x-> infty (1+x^4)/5x+3x^2)
How many solutions does the equation sinx = - sq root(3)/2 have on the interval[0,π]?
none
If s(t) represents the position of an object at time t, then s(t) - s(1)/t-1 represents
the average velocity of the object between time 1 and time t
If v(t)v(t) represents the velocity of an object at time tt, then \displaystyle \lim\limits_{t \rightarrow 1} \frac{v(t) - v(1)}{t - 1}t→1limt−1v(t)−v(1) represents ...
the instantaneous acceleration of the object at time t =1t=1
An object is moving along the xx-axis. Let s(t), v(t)s(t),v(t) and a(t)a(t) be functions giving the position, the velocity and the acceleration of the object at time t.t. Which of the following statements is correct?
the speed of the object at time tt is given by |v(t)|.∣v(t)∣.
sin−1(1/2)=
π/6
Given the graph y = f(x)y=f(x) below, which of the following quantities is the largest? (down thro 4)
∫04f(x)dx
Which of the following statements is true?
∫0x sq root (t^3+1dt) is an antiderivative of sq root x^3+1
Which of the following integrals computes the area of the region that lies above the parabola y=(x−2)^2and below the line y=x?
∫4..1 (−x^2+5x−4)dx
