What is the Maclaurin series expansion of sin(x)?
x - (x^3)/3! + (x^5)/5! - (x^7)/7! + ...
x + (x^3)/3! + (x^5)/5! + (x^7)/7! + ...
1 - x + (x^2)/2 - (x^3)/3 + ...
e^x
Correct Answer :
A. x - (x^3)/3! + (x^5)/5! - (x^7)/7! + ...
Related Questions
If a function f(x) has a local minimum at x = a, what can be said about f'(a) and f''(a)?
f'(a) = 0 and f''(a) < 0
f'(a) < 0 and f''(a) = 0
f'(a) = 0 and f''(a) = 0
f'(a) > 0 and f''(a) > 0
What is the Maclaurin series expansion of sin(x)?
x - (x^3)/3! + (x^5)/5! - (x^7)/7! + ...
x + (x^3)/3! + (x^5)/5! + (x^7)/7! + ...
1 - x + (x^2)/2 - (x^3)/3 + ...
e^x
What is the sum of the first n terms of an arithmetic series with first term a and common difference d?
n(a + d)
n(2a + (n-1)d)/2
n(a + d)/2
a + nd
What is the limit of (x^2 - 1)/(x - 1) as x approaches 1?
1
0
2
undefined
In polar coordinates, what is the equation of a circle with radius r and center at the origin?
r = 1
r = vx^2 + y^2
r = 2?
r = 2
The chain rule states that if y = f(g(x)), then dy/dx is equal to:
f'(x) * g(x)
f'(g(x)) * g'(x)
f(x) * g(x)
f(x) * g'(x)
Which integration technique is used to find the integral of rational functions by decomposing them into partial fractions?
Integration by parts
Trigonometric substitution
Integration by substitution
Partial fraction decomposition
What is the general solution to the differential equation dy/dx + 2y = 4x?
y(x) = 2x^2 + C
y(x) = 2x^2 + 4x + C
y(x) = 2x^2 + 4x
y(x) = 2x^2
A solution to a first-order linear homogeneous differential equation always has:
Two arbitrary constants
One arbitrary constant
No arbitrary constants
Three arbitrary constants
What is the derivative of the function g(x) = e^(3x^2)?
6x * e^(3x^2)
3x^2 * e^(3x^2)
6x * e^(3x)
e^(3x)
What does the second derivative f''(x) tell you about a function f(x)?
The rate of change of f(x)
The concavity of f(x)
The slope of the tangent line to f(x)
The area under the curve of f(x)
What is the radius of convergence for the power series ?(n=0 to 8) (2^n*x^n/n!)?
1
2
8
0
Which of the following is a method for approximating definite integrals using rectangles?
Trapezoidal Rule
Simpson's Rule
Fundamental Theorem of Calculus
L'H�pital's Rule
Which of the following parametric equations represents a horizontal line?
x = t, y = 0
x = 0, y = t
x = t, y = t
x = 0, y = 0
What is the magnitude of the vector <3, 4, 5>?
v6
7
v50
25
Which test can be used to determine the convergence or divergence of a series when the terms are positive, decreasing, and approach zero?
Integral Test
Ratio Test
Alternating Series Test
Divergence Test
What is the sum of the first n terms of an arithmetic series with first term a and common difference d?
n(a + d)
n(2a + (n-1)d)/2
n(a + d)/2
a + nd
What is the order of the differential equation dy/dx = 3x^2 - 2y?
First order
Second order
Third order
Fourth order
The Alternating Series Test can be used to determine the convergence of a series if:
The series terms are all positive.
The series terms alternate in sign and decrease in absolute value.
The series has a finite number of terms.
The series has a constant rate of growth.
Which statement is true about the continuity of a function at a point?
The function must be differentiable at that point.
The function must have a removable discontinuity at that point.
The function must have a jump discontinuity at that point.
The function must have the same limit from the left and right at that point.
What is the limit of (e^x - 1)/x as x approaches 0?
0
1
e
undefined
What is the sum of the infinite geometric series: 1 + 1/2 + 1/4 + 1/8 + ...?
1
2
4
8
What is the limit of (sin(x))/x as x approaches 0?
0
1
p
undefined
What is the nth term of the geometric sequence: 3, 6, 12, 24, ...?
3^n
3^(n+1)
2^n
2^(n+1)
Separation of variables is a technique commonly used to solve which type of differential equation?
Linear differential equations
Exact differential equations
First-order ordinary differential equations
Second-order ordinary differential equations
In polar coordinates, what is the equation of a circle with radius r and center at the origin?
r = 1
r = vx^2 + y^2
r = 2?
r = 2
What is the radius of convergence for the power series ?(n=0 to 8) (2^n*x^n/n!)?
1
2
8
0
What is the derivative of ln(x) with respect to x?
1/x
x
e^x
0
What is the integral of 2x dx?
x^2 + C
x^2
x + C
2x^2 + C
What is the curl of the vector field F(x, y, z) = <2xy, x^2 - y^2, 3z^2>?
<0, 0, 0>
<0, 2z, 0>
<2, -2, 0>
<0, 0, 6z>