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Derivatives
Integrals
Areas/Volume
Limits
Mystery
100
Find the derivative of y= x^2 + 10.
What is 2x?
100
Find the integral for the equation ~ (x^3 + 4) dx.
What is (1/4)x^4 + 4x + C?
100
Let the region R be the region bounded by the graph of y=x^3 and the y-axis from y=0 to y=8.
What is 12?
100
lim x-->infinity (3x^2 -4)/(2-7x-x) .
What is -3?
100
The number of cats Mrs. Mangono has.
What is 6?
200
Find the derivative y= ln(sin x^2).
What is 2x(cot x^2)?
200
Integrate 0~1 (5x^4 + 3x + 9) dx.
What is (x^5 + (3/2)x^2 + 9x) 0|1 = 11 1/2 or 11.5?
200
Let the region R be the region bounded by the graph of y=x^3 and the y-axis from y=0 to y=8. Find the volume of the sold generated when R is rotated around the y-axis.
What is 96/5pi?
200
limx-->0 x/x.
What is 1?
200
Mrs. Mangono's favorite band.
What is Arctic Monkeys?
300
Find the derivative of f(x)= (x^4)(3^x).
What is 4x^3(3^x) + x^4(3^x(ln3))?
300
Integrate ~ (sin^4 x)(cos x) dx. *Use u-substitution.
What is (1/5)(sin^5 x) + C?
300
Let the region T be the region bounded by the graphs of y=x^2-2 and y=4x+3. Find the area.
What is 36?
300
limx-->0 (sin3x)/(sin4x).
What is 3/4?
300
Mrs. Mangono's dogs name.
What is Tallulah?
400
Find the derivative of y = log_2(cos x).
What is (-tan x)/(ln 2)?
400
With v(t)=3x^2 +6t-45 , find the displacement from t=0 and t=5.
What is -25 units?
400
*draw graph on board* Let R be the region in the first quadrant bounded by the graph of y=2 x^(1/2) the horizontal line y=6 and the y-axis, as shown. Find the area of R.
What is 18?
400
lim h-->0 [sin(pi/2 +h) -1]/h.
What is 0?
400
What Mr. Mangono does for a living.
What is makes trophies and awards?
500
Find the derivative of y = e^ln(x^5).
What is 5x^4?
500
Integrate 0~1 (x^4)/(x^5 + 1) dx. *Use u-substitution.
What is (1/5)(ln 2)?
500
With y=2 x^(1/2) and the horizontal y=6. Write, but don't evaluate, an integral expression that gives the volume of the solid generated when R is rotated about the horizontal line y=7.
What is pi 0~9[(7-2x^(1/2))^2 -1] dx?
500
*use L'Hospital Rule* lim x-->0 (sinx)/x.
What is 1?
500
Animal that Mrs. Mangono collects.
What is Moose?