Derivatives
Integrals
Differential
Area/Volume
Limits
100
What is -x^(3)+4x^(2)-5
-3x^(2)+8x
100
What is ∫4/(x^(2)+16) dx
Arctan(x/4)+c
100
dy/dx= 3x/2y given f(0)= 10
y= √((3x^2)/2)+100)
100
area of the region between y=x^2-2 and y=2
-2∫2 (2-(x^2-2)) dx = 32/3
100
Limit of 5x^4+8x^2/ (3x^4-16x^2) as x approaches 0
What is -1/2
200
What is (6x+5)(5x^(2)+4)
Using the product rule: 90x^(2)+50x+24
200
What is ∫xe^(x) dx
xe^(x)-e^(x)+c
200
dy/dx= 4xy^2 given f(0)= 1
y= -1/(2x^2-1)
200
area of the region between y=x^2 and y=4x-x^2
0∫2 ((4x-x^2)-x^2) dx = 8/3
200
Limit of 56x^4+32x^3-59/ (2x^4+16) as x approaches infinity?
What is 56/2 or 26
300
What is (3x+5)^(2)*(x^(5)+4x^(3)+2)
Product Rule: (3x+5)(2x^5+25x^4+60x^3+60x^2+12)
300
What is a∫b cosx dx a= (π)/(2) b= (π)
-1
300
dy/dx= 3x^2y given f(0)= 2
y=2e^(x^3)
300
What is the volume of the region bounded by √x, y=3, and the y-axis about the y-axis.
v= ∫ π y^(4) dy = 243 / 5 π a-0 b-3
300
lim x^3-2x^2+3x-4/(4x^3-3x^2+2x-1) as x approaches infinity
what is 1/4
400
What is ((4x^(3)+5x^(2)+3)^(2))/((20x^(2)+4))
Quotient Rule: ((40x^(2)+8)(12x^(2)+10x)-40(4x^(3)+5x^(2)+3)x)(4x^(3)+5x^(2)+3)/(20x^(2)+4)^(2)
400
What is ∫(x)/( √ (36-x^(4)))
1/2 arcsin (x^(2)/6) + c
400
dy/dx= y^2/x given f(1)= 1/3
y= -1/(lnx-3)
400
What is the volume of the region bounded by y= 2x^(2) and y= x^(3) about the x-axis
v= ∫ π (4x^(4)- x^(6)) dx = 256 / 35π a-0 b-2
400
Limit of (2x-1)(3-x)/(x-1)(x+3) as x approaches infinity
What is -2
500
What is ln(ln(ln x))
Chain Rule: 1/xln(ln(x))ln(x)
500
What is ∫ 2sinx / cos^(3)x
x/cos^(2)x - tanx + c
500
dy/dx= y^2/(x-1) given f(2)= 3
y=1/(1/3-ln(x-1))
500
What is volume of the region bounded by x= y^(2)-6y+10 and x=5 about the y-axis
v= ∫ π (-75+120y-56y^2+12y^(3)-y^(4))dy = 1068/15π a-1 b-5
500
Let f be the function given by f(x)= lnx/x for all x>0. The derivative of f is given by f'(x) = 1-lnx/x^2. Find the limf(x) as x approaches 0+
What is -infinity or does not exist
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