Derivatives
Related rates
Integrals
Grab bag
100
y = x(x^2 - 3)(x^3 + 1) find y'
y'= 6x^5 - 12x^3 + 3x^2 - 3
100
Air is being pumped into a spherical balloon at the rate of 10 cubic inches per minute. Find the rate of change when the radius is 2 inches.
5/8pi
100
Find the integral of 4x^2
What is (4x^3)/3 or (4/3)x^3
100
Find the limit as x approaches -3 |x + 1| + (3/x)
What is 1
200
y= (4x+3)/(3x-1) Determine y' (simplify numerator)
y'= -13/(3x-1)^2
200
If snowball melts so that its surface are decreases at a rate of 3cm^2/min, find the rate at which the radius decreases when the diameter is 10cm. (SA = 4pir^2
-3/40pi
200
Approximate the area under the curve over the given interval using 4 midpoint rectangles. y = −x + 6; [0, 4]
What is 16
200
Use implicit differentiation to find an equation of the tangent line to the curve sinx + cosy = 1 at the point (pi/2 , pi/2)
What is y= pi/2
300
If f(x)= ln(sinx) determine f '(x)
Cotx
300
A camera is located 50 feet from a straight road along which a car is traveling at 100 feet per second. The camera turns so that it is pointed at the car at all times. In radians per second, how fast is the camera turning as the car passes closest to the camera?
-2 rad/sec
300
Find the integral of 2sinx + 3cosx
What is -2cosx + 3sinx + C
300
List the intervals at which f(x) is increasing f(x)= 5 - 6x - (3x^2)
What is (-infinity, -1)
400
f(x)= tan(3^x) find f'(x)
sec^2(3^x)(3^x)(ln(3))
400
Wink the cat would like to eat fish from Jon's fish tank without getting her paws wet. The tank is a super duper cool inverted cone with a diameter of 100 cm and a height of 75 cm. Wink knocks a hole in the bottom tip and water begins leaking out. She notices that the water level is dropping at a rate of .5cm/sec when its depth is 30cm. how fast is the volume of the water leaking out of the tank?
-200 pi
400
Find the integral of (4sinx)/(3tanx)
What is (4/3)sinx + C
400
Find the point(s) of inflection of the graph of f(x)=(x^3)(x-4)
What is (2, -2) & (2, -16)
500
y= sin^5(4x+7) find y'
y' = 20 sin^4(4x+7)cos(4x+7)
500
!!!!!!!!!!DAILY DOUBLE BOYYY!!!!!!!!!!!leaning against the side of a building. If the foot of the ladder is pulled away t=from the building at a constant rate of 8 inches per second, how fast is the area of the triangle formed by the ladder, the building and the ground changing ( in feet squared per second0 at the instant when the top of the ladder is 12 feet above the ground?
199/36 ft^2/sec
500
Find the integral of (3/x)
What is 3ln|x| + C
500
Find the limit as x approaches 0 from the positive direction (e^x)/(1+ln|x|)
What is 0
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