Q. Which of the following functions is not continuous at x = 1?
-
A.
f(x) = x^2
-
B.
f(x) = 1/x
-
C.
f(x) = sin(x)
-
D.
f(x) = { x, x < 1; 2, x >= 1 }
Solution
The function has a jump discontinuity at x = 1, hence it is not continuous.
Correct Answer: D — f(x) = { x, x < 1; 2, x >= 1 }
Learn More →
Q. Which of the following functions is not continuous?
-
A.
f(x) = x^2
-
B.
f(x) = 1/x
-
C.
f(x) = sin(x)
-
D.
f(x) = e^x
Solution
f(x) = 1/x is not continuous at x = 0.
Correct Answer: B — f(x) = 1/x
Learn More →
Q. Which of the following functions is not differentiable at x = 0? f(x) = x^2 sin(1/x) for x ≠ 0 and f(0) = 0.
-
A.
f(x)
-
B.
g(x) =
-
C.
x
-
D.
-
.
h(x) = x^3
-
.
k(x) = x^2
Solution
The function f(x) is not differentiable at x = 0 due to the oscillatory nature of sin(1/x) as x approaches 0.
Correct Answer: A — f(x)
Learn More →
Q. Which of the following functions is periodic?
-
A.
f(x) = x
-
B.
f(x) = cos(x)
-
C.
f(x) = e^x
-
D.
f(x) = ln(x)
Solution
The cosine function is periodic with a period of 2π.
Correct Answer: B — f(x) = cos(x)
Learn More →
Q. Which of the following is a family of exponential curves?
-
A.
y = e^x
-
B.
y = x^2
-
C.
y = log(x)
-
D.
y = sin(x)
Solution
The equation y = e^x represents a family of exponential curves for different bases.
Correct Answer: A — y = e^x
Learn More →
Q. Which of the following is a necessary condition for a function to be continuous at a point?
-
A.
The function must be defined at that point
-
B.
The function must be differentiable at that point
-
C.
The function must be bounded
-
D.
The function must be increasing
Solution
A function must be defined at a point to be continuous there.
Correct Answer: A — The function must be defined at that point
Learn More →
Q. Which of the following is a necessary condition for f(x) to be continuous at x = a?
-
A.
f(a) exists
-
B.
lim x->a f(x) exists
-
C.
lim x->a f(x) = f(a)
-
D.
All of the above
Solution
All conditions must be satisfied for f(x) to be continuous at x = a.
Correct Answer: D — All of the above
Learn More →
Q. Which of the following is a one-to-one function?
-
A.
f(x) = x^2
-
B.
f(x) = 2x + 3
-
C.
f(x) = sin(x)
-
D.
f(x) = e^x
Solution
A function is one-to-one if it never takes the same value twice. f(x) = 2x + 3 and f(x) = e^x are one-to-one.
Correct Answer: B — f(x) = 2x + 3
Learn More →
Q. Which of the following is a purely imaginary number?
-
A.
2 + 3i
-
B.
0
-
C.
4
-
D.
0 + 5i
Solution
A purely imaginary number has no real part, so 0 + 5i is purely imaginary.
Correct Answer: D — 0 + 5i
Learn More →
Q. Which of the following is a root of the equation z^2 + 1 = 0?
Solution
The roots are z = ±i.
Correct Answer: A — i
Learn More →
Q. Which of the following is a subset of {1, 2, 3}?
-
A.
{1, 2}
-
B.
{4}
-
C.
{1, 2, 3, 4}
-
D.
{2, 3, 4}
Solution
A subset is a set that contains elements from another set. {1, 2} is a subset of {1, 2, 3}.
Correct Answer: A — {1, 2}
Learn More →
Q. Which of the following is a subset of {x, y, z}?
-
A.
{x, y}
-
B.
{x, y, z, w}
-
C.
{y, z, w}
-
D.
{x, y, z, x}
Solution
A subset can only contain elements that are in the original set. {x, y} is a valid subset of {x, y, z}.
Correct Answer: A — {x, y}
Learn More →
Q. Which of the following is an even function?
-
A.
f(x) = x^3
-
B.
f(x) = x^2
-
C.
f(x) = sin(x)
-
D.
f(x) = tan(x)
Solution
An even function satisfies f(x) = f(-x). f(x) = x^2 is even.
Correct Answer: B — f(x) = x^2
Learn More →
Q. Which of the following is an identity?
-
A.
sin^2 x + cos^2 x = 1
-
B.
tan x = sin x / cos x
-
C.
sec x = 1/cos x
-
D.
All of the above
Solution
All the given options are trigonometric identities.
Correct Answer: D — All of the above
Learn More →
Q. Which of the following is equivalent to log_a(b^c)?
-
A.
c * log_a(b)
-
B.
log_a(b) / c
-
C.
log_a(c) + log_a(b)
-
D.
log_a(b) - c
Solution
log_a(b^c) = c * log_a(b) by the power rule of logarithms.
Correct Answer: A — c * log_a(b)
Learn More →
Q. Which of the following is NOT a family of curves?
-
A.
y = kx^2
-
B.
y = ksin(x)
-
C.
y = kx
-
D.
y = k/x
Solution
y = kx represents a family of straight lines, but it is not a family of curves.
Correct Answer: C — y = kx
Learn More →
Q. Which of the following is not a subset of {a, b, c}?
-
A.
{a}
-
B.
{b, c}
-
C.
{a, b, c}
-
D.
{d}
Solution
The set {d} does not contain any elements from {a, b, c}, so it is not a subset.
Correct Answer: D — {d}
Learn More →
Q. Which of the following is not continuous at x = 0?
-
A.
f(x) = x^3
-
B.
f(x) = e^x
-
C.
f(x) = 1/x
-
D.
f(x) = ln(x)
Solution
f(x) = 1/x is not continuous at x = 0 as it is undefined there.
Correct Answer: C — f(x) = 1/x
Learn More →
Q. Which of the following is the correct identity for sin(2A)?
-
A.
2sinAcosA
-
B.
sin^2A + cos^2A
-
C.
sinA + cosA
-
D.
sinAcosA
Solution
The double angle formula states that sin(2A) = 2sinAcosA.
Correct Answer: A — 2sinAcosA
Learn More →
Q. Which of the following is the equation of a hyperbola with transverse axis along the x-axis?
-
A.
x^2/a^2 - y^2/b^2 = 1
-
B.
y^2/a^2 - x^2/b^2 = 1
-
C.
x^2/b^2 - y^2/a^2 = 1
-
D.
y^2/b^2 - x^2/a^2 = 1
Solution
The equation of a hyperbola with transverse axis along the x-axis is x^2/a^2 - y^2/b^2 = 1.
Correct Answer: A — x^2/a^2 - y^2/b^2 = 1
Learn More →
Q. Which of the following is the equation of an ellipse with foci at (0, ±c) and vertices at (0, ±a)?
-
A.
x^2/a^2 + y^2/b^2 = 1
-
B.
y^2/a^2 + x^2/b^2 = 1
-
C.
x^2/b^2 + y^2/a^2 = 1
-
D.
y^2/b^2 + x^2/a^2 = 1
Solution
The equation of an ellipse with foci at (0, ±c) and vertices at (0, ±a) is y^2/a^2 + x^2/b^2 = 1.
Correct Answer: A — x^2/a^2 + y^2/b^2 = 1
Learn More →
Q. Which of the following is the range of the function f(x) = x^2 - 4?
-
A.
(-∞, -4]
-
B.
[-4, ∞)
-
C.
(-4, ∞)
-
D.
[0, ∞)
Solution
The minimum value of f(x) is -4 when x=0, so the range is [-4, ∞).
Correct Answer: B — [-4, ∞)
Learn More →
Q. Which of the following is the range of the function f(x) = x^2?
-
A.
All real numbers
-
B.
All positive real numbers
-
C.
All non-negative real numbers
-
D.
All integers
Solution
The function f(x) = x^2 is non-negative for all real x, hence the range is all non-negative real numbers.
Correct Answer: C — All non-negative real numbers
Learn More →
Q. Which of the following is the range of the function f(x) = |x - 1|?
-
A.
(-∞, 1)
-
B.
[0, ∞)
-
C.
(-1, 1)
-
D.
[1, ∞)
Solution
The minimum value of |x - 1| is 0 when x = 1, so the range is [0, ∞).
Correct Answer: B — [0, ∞)
Learn More →
Q. Which of the following is the solution set for the inequality x + 2 > 1?
-
A.
x > -1
-
B.
x < -1
-
C.
x > 1
-
D.
x < 1
Solution
x + 2 > 1 => x > -1.
Correct Answer: A — x > -1
Learn More →
Q. Which of the following is the solution set for the inequality x + 2 > 7?
-
A.
x > 5
-
B.
x < 5
-
C.
x > 9
-
D.
x < 9
Solution
x + 2 > 7 => x > 5.
Correct Answer: A — x > 5
Learn More →
Q. Which of the following is the solution set for the inequality x + 5 > 2?
-
A.
x > -3
-
B.
x < -3
-
C.
x > 3
-
D.
x < 3
Solution
x + 5 > 2 => x > -3.
Correct Answer: A — x > -3
Learn More →
Q. Which of the following is the solution set for the inequality: 3x + 2 > 11?
-
A.
x > 3
-
B.
x < 3
-
C.
x > 2
-
D.
x < 2
Solution
3x + 2 > 11 => 3x > 9 => x > 3.
Correct Answer: A — x > 3
Learn More →
Q. Which of the following is the solution to the inequality 3x + 2 ≥ 11?
-
A.
x < 3
-
B.
x > 3
-
C.
x ≤ 3
-
D.
x ≥ 3
Solution
3x + 2 ≥ 11 => 3x ≥ 9 => x ≥ 3.
Correct Answer: D — x ≥ 3
Learn More →
Q. Which of the following is the solution to the inequality x + 2 > 7?
-
A.
x < 5
-
B.
x > 5
-
C.
x < 9
-
D.
x > 9
Solution
x + 2 > 7 => x > 5.
Correct Answer: B — x > 5
Learn More →
Showing 2791 to 2820 of 2847 (95 Pages)
