BC Calculus Memorization Test Preparation
Name:
Section 1 - Limits
1) A function f(x) is continuous at x = c iff:
a)
b)
c)
2) If f(x) and g(x) are polynomials, the limit as x → ∞ of f(x)/g(x) = ?
a) Case 1:
b) Case 2:
c) Case 3:
3) State two important trigonometric limits.
4) State the limit definition of the derivative.
5) If you take the limit of a function as x → ∞, what are you are trying to
locate?
6) The limit of f(x) does not exist at x = c if:
a)
b)
c)
Section 2 - Derivatives
1) State the power rule.
2) State the product rule.
3) State the quotient rule.
4) State the chain rule.
5) What is the derivative of sinx?
6) What is the derivative of cosx?
7) What is the derivative of tanx?
8) What is the derivative of cscx?
9) What is the derivative of secx?
10) What is the derivative of cotx?
11) What is the derivative of eu?
12) What is the derivative of au?
13) What is the derivative of lnu?
14) What is the derivative of logau?
15) What is the derivative of arcsinu?
16) What is the derivative of arccosu?
17)What is the derivative of arctanu?
18) What are critical numbers?
19) What are the only places where the absolute extrema of a function can
be located on a closed interval?
20) What are possible points of inflection? What are points of inflection?
21) When is a function increasing/decreasing?
22) When is a function concave up/concave down?
23) State the first derivative test.
24) State the second derivative test.
25) State the formula for finding g'(a) if g(x) and f(x) are inverses.
26) State the parametric formulas for
𝑑𝑦
𝑑𝑥
&
𝑑2𝑦
𝑑𝑥 2
.
27) State the parametric formula for speed.
28) State the formula for
𝑑𝑦
𝑑𝑥
for the polar function 𝑟 = 𝑓(𝜃).
29) State formulas for finding xn+1 and yn+1 using Euler’s Method.
30) State L’Hopital’s Rule.
Section 3 - Integration
1) State the antiderivative of sinx.
2) State the antiderivative of cosx.
3) State the antiderivative of tanx.
4) State the antiderivative of cscx.
5) State the antiderivative of secx.
6) State the antiderivative of cotx.
7) State the antiderivative of ex.
8) State the antiderivative of ax.
9) State the antiderivative of 1/x.
10) State 3 key properties of definite integrals.
a)
b)
c)
11) State the formula for the average value of a function.
12) State the Trapezoidal Rule.
13) State the formula for the area bounded between two curves.
14) State the formula for the volume of the solid of revolution created by
revolving around a horizontal axis. (Disc method)
15) State the formula for the volume of the solid of revolution created by
revolving around a horizontal axis. (Washer method)
16) State the formula for the volume of a solid of revolution created by
revolving around a horizontal axis. (Shell method)
17) State the formula for integration by parts.
18) State the formula for the area of a polar region.
19) State the formula for length of a curve.
20) State the parametric formula for length of a curve.
21) State the polar formula for length of a curve.
22) State two common forms a logistic differential equation can take.
Define the most important parameter.
Section 4 – Sequences and Series
1) State the formula for the sum of a geometric series.
2) State the form of a p-series and when it converges or diverges.
3) State the alternating series test.
4) State the alternating series error bound.
5) State the integral test.
6) State the ratio test.
7) State the direct comparison test.
8) State the limit comparison test.
9) State the formula for an nth Taylor Polynomial of f(x) at x = c.
10) State the Maclaurin series for ex.
11) State the Maclaurin series for sinx.
12) State the Maclaurin series for cosx.
13) State the Maclaurin series for
1
1−𝑥
.
14) State the Lagrange error bound for an nth Taylor polynomial.
Section 5 – Theorems
1) State the Intermediate Value Theorem.
2) State the Mean Value Theorem.
3) State the Extreme Value Theorem.
4) State the Fundamental Theorem of Calculus.
5) State the Second Fundamental Theorem of Calculus.