Algebra
Solve for x:
2x + 3 = 9
x = 3
Evaluate:
sin(45)
sqrt(2)/2
The operation used to find the instantaneous rate of change or the slope of a tangent line to a curve.
What is differentiation? (or What is a derivative?)
Find the limit as x approches 0:
sin(x)/x
limit = 1
Find the derivative of the vector valued function:
r(t) = <t2, sin(t), et>
r'(t) = <2t, cos(t), et>
x2 - 5x + 6
x = 2 and x = 3
Find the equation of the line that passes through the points (2,3) and (4,7).
y = 2x - 1
Formula for the rate of change of x with respect to y.
What is dx/dy?
(2x + 1)dx
12
Find the integral of the vector valued function with the initial condition <1,2,1>:
r(t) = <2t, cos(t), et>
r'(t) = <t2 + 1, sin(t) + 2, et + 1>
Find the discriminant of x2-6x+11 = 0
What is -8
Simplify the complex number:
(3 + 2i)(4 - 5i)
22 - 7i
Solve y=4x5+2x3+4x2 with respect to x.
*Find d4y/dx4
What is 480x?
Use implicit differentiation to find dy/dx:
x2 + xy + y2 = 7
dy/dx = (-2x-y)/(x+2y)
Solve the integral using integration by parts:
(xex)dx
xex - ex + C
Common ratio: 2
Find the domain:
f(x) = sqrt(5-x)
x is less than or equal to 5
The slope of chord formula.
*Hint not y2-y1/x2-x1
What is f(x+∆x)-F(x)/∆x?
Find the derivative:
f(x) = e2xsin(x)
f'(x) = 2e2xsin(x) + e2xcos(x)
Find the arc length of the curve given the parametric equations x = 3t2 and y = 2t3 from t = 0 to t = 1.
7sqrt(14) - 4
Solve for x:
log2(x-1) + log2(x+1) = 3
x = 3
Extraneous: x = -3
Determine the polar coordinates of the point with Cartesian coordinates (-4, 4/sqrt(3)) where r is positive and 0 ≤ θ < 2pi.
(8(sqrt3)/3, 5pi/6)
Contributors to Differential Calculus.
Who are Augustin Louis Cauchy (1789–1857), Bernhard Riemann (1826–1866), and Karl Weierstrass (1815–1897)?
Determine the area of the region bounded by y = x2 and y = 4x - x2.
Evaluate the improper integral with bounds from 1 to infinity:
(ln(x)/x2)dx
-1