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Miscellaneous
Derivatives
Trigonometry
Algebra
Integration
100
Find the limit as x goes to positive infinity of (3x + 2)/(2x - 1)
What is 3/2
100
What is the first derivative of y = pi*x
What is pi.
100
Give the exact value for cos(pi)
What is -1
100
Give an equation for the function shown in EXAMPLE #1 (See attached Powerpoint)
What is y = ln(x) OR y = log(x)
100
Find the integral of e^(4x)
What is (1/4)e^(4x) + C
200
Integrate (16x + 20)/(2x^2 + 5x - 7)
What is 4*ln|2x^2 + 5x - 7| + C
200
Find the first and second derivatives of y = 5cos(3x)
What is: y' = -15sin(3x) y" = -45cos(3x)
200
Give the exact value of cos(4pi/3)
What is -1/2
200
Evaluate ln(1)
What is 0
200
Find the integral of x^2 / sqrt(x^3 - 1)
What is (2/3)sqrt(x^3 - 1) + C
300
What is the first derivative of (sin(x))^3 - cos(x^3)
What is 3(sin(x))^2*cos(x) + 3x^2*sin(x^3)
300
Find the first derivative of y = e^(x^2)
What is 2x*e^(x^2)
300
What is the range of y = arcsin(x)
What is [-pi/2 , pi/2]
300
Give an equation for the function shown in EXAMPLE #2 (see powerpoint)
What is y = e^x
300
What is the integral of tan(x)
What is -ln|cos(x)| + C
400
Integrate e^(1/x) / x^2
What is -e^(1/x) + C
400
Find the first derivative of y = tan(sin(2x^3))
What is 6x^2*cos(2x^3)*(sec^2)(sin(2x^3))
400
Name all 3 Pythagorean Identities
What is: (1) (sin(x))^2 + (cos(x))^2 = 1 (2) 1 + (tan(x))^2 = (sec(x))^2 (3) (cot(x))^2 + 1 = (csc(x))^2
400
Simplify to so single logarithmic term: 3ln(2) + ln(4)
What is ln(32)
400
What is the integral of sec(x/2)tan(x/2)
What is 2sec(x/2) + C
500
Integrate (x + 2)/(x + 1)
What is x + ln|x + 1| + C
500
Find the first derivative of arctan(x^3)
What is 3x^2 / (1 + x^6)
500
Solve the equation for x. 2sin(2x) - 1 = 0 for x in [0,2pi]
What is pi/12 , 5pi/12 , 13pi/12 , 17pi/12
500
Complete the square -x^2 + 4x - 13
What is -(x - 2)^2 - 9
500
What is the integral of 2/(x*sqrt(x^2 - 9))
What is (2/3)arcsec(|x|/3) + C