Calculus
Solve for x: 2−3x>1and−4<2x+1
(-5/2, 1/3)
Lim x->2 + (x^2 + 3x -4)/(x-2)
+ infinity
The radius of a circle is decreasing at a constant rate of 0.2 mm/sec. In terms of the circumference, C, what is the rate of change of the area of the circle in mm2/sec?
- 0.2 C
The area of a square is increasing at the rate of 4 square inches per minute. Find the rate at which a side is increasing when the side is 3 inches.
.67 in/min
Use the graph of f(x) to evaluate the limit : lim x-> 1 - f(x) =
0
Lim x-> 0 (cot x)/(csc x) =
1
Use the graph of f(x) to evaluate the limit. limx→2f(x)= (straight lines)
1
A bicycle path and a road cross at right angles. A police woman stands on the road 70 meters south of the crossing and watches an eastbound cyclist traveling at 6 meters per second. At how many meters per second is the cyclist moving away from the police woman 4 seconds after passing the intersection?
1.95 m/sec.
The radius of a circle is increasing at a constant rate of 0.4 feet/sec. What is the rate of increase in the area of the circle at the instant when the circumference of the circle is 40π feet?
16π ft2/second
Find the average rate of change of the function f(x)=x2−2x+3on the interval [−1,5]
2
Use the graph of f(x) to evaluate the limit. limx→1+f(x)= (straight line)
2
The height h of a right circular cone is 20 cm and is decreasing at the rate of 4 cm/sec. At the same time, the radius r is 10 cm and is increasing at the rate of 2 cm/sec. What is the rate of change of the volume in cm3/sec? (Note: The volume of a right circular cone is V = \frac13\mathrm\pi\;\mathrm r^2\mathrm h31πr2h.)
400pi/3
Lim x-> 2 + {2x-3, x <2, x^2 + 1 , x >or equal 2}
5
Find an equation for the line through (2,7) and perpendicular to y = (4/5)x-3
5x + 4y = 38
Lim x->0 ((x*3) ^2 -9)/ (x) =
6
limx→0(sin(7x))/(x) =
7
A function is decreasing if
As x moves to the right, the graph moves down
A function is increasing if
As x moves to the right, the graph moves up
Given the graph of f(x) above, which of the following represents f(1/2x)?
B) Widest graph
Which of the following steps should be used to find the intervals on which a function is increasing or decreasing?
Both A and B
If limx->a f(x) exists, then f(a)f(a) exists.
False
True or False: A limit can always be calculated by substituting the value into the function.
False
True or False: It is possible to tell if lim x→4 f(x) exists by only examining f(x) for x close to but greater than 4.
False
Let f(x) = { (x^2 +x) x=/0 , 1 x =0} Which of the following statements are true: I. f(0) exists. II. Lim x->0 f(x) exists III. f is continuous at x=0
I, II, and III
Which of the following functions are one-to-one? I. Y= x^2 + 3 II. Y= x^5-2 III. Y = 2^x-1
II and III only
Let f be a function whose second derivative exists on an open interval I. Then
If f ''(x) = 0 for all x in I, then the graph of f is neither concave up nor concave down.
Let f be a function whose second derivative exists on an open interval I. Then
If f ''(x) > 0 for all x in I, then the graph of f is concave upward
Use the graph of f(x) to evaluate the limit. limx→2f(x) = (curved lines)
Undefined
Use the graph of f(x) to evaluate the limit: lim x->1 f(x) =
Undefined
Which of the following points of discontinuity of f(x) = (x(x-1)^2 (x-2)^2 (x-3)^2)/ (x(x-1)^3(x-2)^2 (x-3) is not removable
X= 1
Identify all the of vertical asymptotes of the graph of y= cot(2x)
X=n • pi/2
The figure above shows the graph of one full period of a sine function. Which of the following is an equation for the graph?
Y=3sin(pi/2 x)
Solve for x: |x+5|≤7
[−12,2]
Fill in the Blank: In determining intervals where a function is increasing or decreasing, you first find domain values where __________________________ will occur; then, test all intervals in the domain of the function to the left and to the right of these values to determine if the derivative is positive or negative.
all critical points
If the radius r and volume V of a sphere are differentiable functions of t, write an equation that relates dV/dt to dr/dt. The volume of a sphere is (4/3)π r3.
dV/dt = 4π r2 dr/dt
Identify the function graphed below:
g(x) = sqrt (4-x)
Complete the sentence: Let f be twice differentiable on an open interval, I. The graph of f is concave downward on I if f '
is decreasing on the interval
Complete the sentence: Let f be twice differentiable on an open interval, I. The graph of f is concave upward on I if f '
is increasing on the interval
If f(x) = 3/(x-1) and g(x) = 2x then the solution set of f(g(x)) = g(f(x)) is
{1/3}
Let f(x) = sqrt (4-x) and g(x) = sqrt (6-x). What is the domain of f(g(x))?
{x: −10≤x≤6}
What is the domain of the function f(x) = (sqrt x^2 -9) / (x-5)
{x: ∣x∣≥3 and x =/5}
Use a calcuator to find all real zeros of f(x)= x^3 -8x^2 +5x +1
{−0.159,0.863,7.296}
