Derivatives
Applications of Derivatives
Integrals
Applications of Integrals
Limits
100
y=x^(-3/4)
What is -3/4 x^(-7/4)
100
How would you justify a local min in a free response question.
What is f'(x)=0 or undef and f' changes - to +
100
Complete the following: if F(x) = g'(x), then ∫F(x) dx from a to b =
What is g(b) - g(a)
100
What does the integral represent graphically? What does the integral represent numerically?
What is Area under the curve and net change
100
What is the formal definition of continuity?
What is 1. the limit exists 2. the value exists 3. the limit is equal to the value
200
f(x)=3x^2 - 4x + 1
What is 6x - 4
200
What is the tangent line to 1/x at x = 1
What is y = 1 - 1 (x - 1)
200
What is true of an odd function ∫f(x)dx from -a to a
What is 0
200
What formula do you use for a question worded: " find the average value of f(x) from x = a to x = b"
What is 1/(b - a) ∫f(x) dx from a to b
200
What are the 3 types of discontinuities? Bonus explain what each is in terms of the definition of continuity
What is jump, removable, vertical asymptote
300
y = 2e^x + x^2
What is 2e^x + 2x
300
x - x^2 y + y = 5x
What is (4 + 2xy)/(1 - x^2)
300
Find ∫(1+3x^2) dx from a = 0 to b = 2
What is 10
300
Find d/dx (∫sin (3t) dt) from a = 2 to b = 3x
What is 3 sin (9x)
300
lim x->3 (x^2 + 5x)/(x + 9)
What is 2
400
f(x) = (x^2 + 1) / (5x - x^2)
What is (2x (5x - x^2) - (5 - 2x)(x^2 + 1))/(5x - x^2)^2
400
2^(x^2)
What is 2x * ln 2 * 2^(x^2)
400
Find ∫(5x^2 + 2 x^(1/2) ) dx
What is 5/3 x^3 + 4/3 x^(3/2) + C
400
Find ∫3x e^(x^2) dx
What is 3/2 e^(x^2) +C
400
lim t->0 (e^t - 1 - t)/(t^2)
What is 1/2
500
y = (ln (w^4 - 1))^3
What is 3(ln (w^4 - 1))^2 ((4w^3)/(w^4 - 1))
500
f(x)=e^x If g(x) is the inverse of f(x), find g'(1)
What is 1
500
Find ∫(x+1)/x dx
What is x + ln (abs(x)) +C
500
Find ∫ ln (x) / x dx
What is 1/2 (ln (x) )^2 + C
500
lim x->0 x sin(1/x) =
What is 0 * Squeeze Thm
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