Unit 1-Limits
A POD forms when both the numerator and denominator share this aspect
Common factor
Along with corner, cusp, and a discontinuity, a function is non-differentiable at this feature
Vertical tangent
When can we use L’Hopital’s Rule
When the limit is indeterminate
The approximation of area under a curve using a finite number of rectangles is called this kind of sum.
Riemann Sum
Evaluate
lim x + 5
x -> 4 x - 4
DNE
The derivative of y = (9x + 3)3
27(9x + 3)2
y' if y = cos(5x)
y' = -5 sin(5x)
Find the antiderivative of f(x) = 4x
F(x) = 2x2 + c
Determine
lim 5x2 + 16x + 3
x -> ∞ 9x2 - 4
5 / 9
The equation of the tangent line to y = 5/(x - 4) at x=-6, in point-slope form
y + 1/2 = -1/20 (x + 6)
Find the derivative of
y = (3x + 5)13 log(1)
(7 - 4x)9
0
Find the antiderivative of x cos(2x2)
1/4 sin(2x2) + c
Find the value k for which the limit exists:
lim -4x2 + kx + 7k - 6
x -> 3 2x2 - 5x - 3
k = 3
Find dy/dx of
x2 = x - y
x + y
dy/dx = y/x - (x + y)2
Determine where the slope of y = e2x + 3 is the same as the y-coordinate
x = ln(3) / 2
Evaluate the integral of (x3 + 2)1/2 x2 dx
2/9 (x3 + 2)3/2 + c