Evaluate the indefinite integral 6x^5 - 18x^2 +7 dx
What is x^6 -6x^3 +7x + c
100
The formula of the derivative of (cscu)
What is -(cscucotu) * derivative of u
(* is multiplication)
100
The critical points of f(x)= 8x^3 + 81x^2 -42X -8
What is x=-7 and x=1/4
200
lim x->4 (x^2 - 16)/ (2x - 8)
(-> is an arrow)
What is 4
200
The derivative of f(x)= 6x^3 -9x +4
What is f^1(x) = 18x^2 - 9
200
Evaluate the definite integral 40x^3 +12x^2 -9x +14 dx
What is 10x^4 +4x^3 -(9/2)x^2 +14x + c
200
The formula of the derivative e^u
What is e^u * the derivative of u
(* is multiplication)
200
Determine all the number(s) c which satisfy the conclusion of Rolle’s Theorem for the given function and interval. (Mean value theorem)
f(x)=x^2 -2x -8 on [-1,3]
What is c=1
300
Vertical Asymptote at f(x)= (7x)/(10-3x)^4
What is x=10/3
300
The derivative of g(z)= 4z^7 -3z^(-7) + 9z
What is g^1(z)= 28z^6 + 21z^(-8) + 9
300
Evaluate the indefinite integral (8x-12)(4x^2 -12x)^4 dx
What is (1/3)(4x^2 - 12x)^5 + C
300
The formula of the derivative (arctanu)
What is 1/(1+u^2) * the derivative of u
(* is multiplication)
300
Find two positive numbers whose sum is 300 and whose product is a maximum. (Optimization)
What is x=150 and y=150
400
Evaluate the existence
For limx->2 = (x+7)/(x^2 - 4)
What is a limit that does not exist.
400
The derivative of h(u)= tan(4+10u)
What is h^1(u)= 10sec^2(4+10u)
400
Evaluate the indefinite integral 90x^2sin(2+6x^3) dx
What is -5cos(2 + 6x^3) + C
400
The ln(1)
What is 0
400
Determine the critical points of g(x)=x^6 -2x^5 +8x^4
What is x=0
500
Given: the lim x->8 f(x)=9
the lim x->8 g(x)=2
the lim x->8 h(x)=4
Find x->8 [g(x)h(x) - f(x)]
What is 17
500
The derivative of y= [sin(3t)]/(1+t^2)
What is y^1= [3cos(3t)(1+t^2) - 2tsin(3t)]/ (1+t^2)^2
500
Evaluate the definite integral (3x)/(1+9x^2)^4 dx
What is (-1/18)[1/(1+9x^2)^3] + c
500
The formula of the integral sec^2 (x) dx
What is -tanx + C
500
Determine the area of the largest rectangle that can be inscribed in a circle of radius 1. (Optimization)