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Calculus Review Showdown (through derivatives) Flashcards | StudBud
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Calculus Review Showdown (through derivatives)
Calculus Review Showdown (through derivatives)
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1
sin
2
x + cos
2
x =
1 - csc2 x
0
1
tan2 x
2
2 times 3 equals
8
5
6
4
3
What is sin (2pi / 3) ?
1/2
- √3 / 2
- 1/2
√3 / 2
4
If f(x) has a jump discontinuity at x = 4,
the limit as x approaches 4 equals the function value
the limit as x approaches 4 does not exist
f(4) does not exist
f(x) must be a piecewise-defined function
5
The intermediate value theorem
states that a zero must exist on a closed interval
helps to identify oscillating functions
is true only for increasing functions
requires that the fn must be continuous on the interval
6
Differentiate y = csc
2
x + cot
2
x
- csc2 x( csc2 x + cot2 x)
cot x + csc4 x
0
-4 csc2 x cot x
7
Which statement is true?
f(x) = |x| is differentiable for all real numbers
Continuity implies differentiability
If f(a) does not exist, the limit at x = a does not exist
d/dx (f(x) g(x)) ≠ f'(x) g'(x)
8
What is the limit of (√x -2) / (x - 4) as x approaches 4?
0
1/4
DNE
4
9
Find f'(x) if f(x) = cot
3
(√x)
(-3 cot2 √x ) / (2 √x)
(cot2 √x (csc2 √x)) / (2 √x)
None of these
(-3 cot2 √x (csc2 √x)) / (2 √x)
10
The line perpendicular to a curve at a given point is
a tangent line
a secant line
an abnormal line
a normal line
11
To compute average rate of change over a given interval
you use the tried and true slope formula
you guess
Take the average of the slopes at the endpoints
you use the derivative
12
Which of the following is NOT true about f(x) = sqrt ( x
2
- 49 )?
f is continuous over ( -∞, -7]
f is continuous at x = 14
f is continuous on the interval [ -7, 7 ]
None of these
13
If s(t) = ( t
3
+ 1)
2
(feet/second), find the acceleration at 1 second.
0 ft/sec2
12 ft/sec2
42 ft/sec2
4 ft/sec2
14
If the first derivative changes from positive to negative at x = a, the graph of the function
has a zero at x = 0
is undefined at x = a
has a horizontal tangent at x = a
has a local minimum at x = a
15
What is more fun than calculus?
Dental surgery without anesthetic
Nothing could be more fun than calculus!
Having the flu
Going to the DMV
16
If f(x) = (3x + 2) / (5x - 1), what is f
-1
(x)?
DNE
(x + 3) / (5x - 2)
((5x - 1)(3) - (3x + 2)(5)) / (5x - 1)2
None of these
17
The water level is dropping at a rate of __________ when the diameter is 2 inches.
1/(2π) in/sec
1/π in/sec
2/π in/sec
π in/sec
18
Find the equation of the tangent line to the curve y
4
+ xy = x
3
- x + 2 at the point (1, 1)
y = 1 = 5 ( x - 1)
y - 1 = 1/5 (x - 1)
y - 1 = 2/5 (x - 1)
y - 1 = 2/7 (x - 1)
19
What is the derivative of e
sin(2x)
?
2esin(2x)cos(2x)
(sin 2x)(esin(2x) - 1)
e2cos(2x)
esin(2x)
20
f(x) = 1 / (x + 1) and g(x) = x
2
- 5. Find all values of x where f(g(x)) is discontinuous.
-1
-2, 2
-1, √5
√5
21
Multiply and simplify: (2 - i)(4 + 3i)
i don't know
14 + 2i
8 - i
11 + 2i
22
Equation of the line tangent to f(x) = sqrt (2x + 1) at the point (4, 3).
x - 3y - 5 = 0
x - 3y + 5 = 0
x + 3y + 5 = 0
None of these
23
Find the vertical asymptote(s) of f(x) = ( x
2
- x - 2) / ( x
2
+ x - 6)
x = 3
x = -2
x = -3
x = 2
24
Evaluate the derivative of 5x
2
- 3xy + y = 2 at the point (0, 2).
-5/4
-2
0
6
25
What is the second derivative of g(x) = x cos x ?
-2 sin x - x cos x
- x sin x + cos x
-x sin x
This answer is wrong!
