Show:
Limits
Derivatives
Derivatives Part 2
Integrals
Antiderivatives
100
lim x→−3 x^2-x-12/x+3
What is -7
100
Find the derivative of the function: y= 5 secxtanx
What is y'= 5 secx (2tan^2x+1) or y'= 5 secx (tan^2x +sec^2x)
100
d [(3x-2x^3)(5+4x)] -- dx
What is (3 - 6x^2)(5+4x) + (3x-2x^3)(4)
100
Integrate: ∫1/(x^2) dx
What is -1/x + C
100
∫ 15x^4 dx
What is 3x^5+C
200
lim (2+h)^2 - 4/ h h->0
What is 4
200
Find the derivative of the function: g(x)= 3xsin^2x/x^2 cos x
What is (x^2cosx)((3sin^2x)+(6xsinxcosx)) - (2xcosx - x^2sinx)/(x^2cosx)^2
200
d/dx [5x^3*sinx]
What is 15x^2(sinx)+5x^3(cosx)
200
∫ sin x dx
What is -xcosx + sinx +C
200
∫ -3x^2 dx
What is -x^3 +c
300
lim 3- √t/ t->9 9 - t
What is 1/6
300
y= (2x^2 +5) ^7
What is y'=28x(2x^2 +5)^6
300
d/dx(3z^2-4z)
What us (6z-4)(dz/dx)
300
Integrate: ∫lnx/x dx
What is (lnx)^2/2 + C
300
∫ 2/(z^2) dz
What is -2/z +c
400
lim 1/w - 1/2 / w->2 w-2
What is -1/4
400
Find the derivative of the function: f(x)= 7 ^ 1/x
What is f(x)= -ln7*7^1/x / x^2
400
d/dx (3t^5 cost -2t^9)
What is (15t^4 - 3t^5sint-18t^8)(dx/dt)
400
The integral that represents the area of a semicircle whose flat side lies on the x-axis from 2 to 6.
What is integral (sqrt(4 - x^2)) dx
400
∫ cotx (sinx) dx
What is sinx+C
500
lim cos [3pi/2 + x]- cos[3pi/2] / x->0 x
What is 1
500
Find the derivative of the function: y= arccos [x/3]
What is y'= -√9-x^2
500
Is f(x)= { |x-2| for x<2 (x-3)^2-1 for x=> 2 continuous?
what is no because the values don't exist at the same points
500
Integrate: ∫ 1 + (tanx)^2 dx
What is tanx + C
500
∫ (7t+8)^3 dt
What is (7t+8)^4 ----------- + C 28