Limits
lim(x->𝝅) sin(x)/cos(x)
What is sqrt(3)?
d/dx (3x^5-6x^4+x^2+4x^3+2)/2
What is 15x^4/2 - 24x^3/2 + 12x^2/2 + 2x/2
A particle starts with an initial velocity of -10m/s. The particle accelerates at a rate of 5 m/s^2. What is the graph's concavity?
What is concave up?
integral(a=0, b=𝝅; sin(x)dx)+ integral(a=𝝅, b=3𝝅/2; sin(2x)dx)
What is 3
Does f(x) = 2x^5-6x in the interval [1,2] go through f(x) = 38?
1 version of the limit definition of a derivative
lim(x->h) f(x+h)-f(x)/h
lim(x->a) f(x)-f(a)/(x-a)
dy/dx e^(2ln(x))
What is 2x
For a concave down graph, will a tangent line under or over approximate?
What is overapproximate
Integral(a=2,b=0; e^2xdx)
Does f(x) = 3x^6-2x^3 have a zero from [0.5,1]?
What is by IVT, a zero exists for f(x) on [0.5,1]?
lim(x->-∞) (5e^x-2)/(3^x-6)
What is 1/3
f(x) = tan(3x)cos(x)
Find f'(x)
What is 3sec^2(3x)cos(x)-tan(3x)sin(x)
The difference between a critical point and a max/min
What is f'(x) crosses 0?
d/dx[Integral(a=0,b=x; tan(3t)dt)]
What is tan(3x)
What is differentiable?
lim(x->5) 2(x-5)/(x^2-2x-15)
What is 1/4
g(x) = f^-1(x)
f(x) = 4x^2+3
The derivative of g(x) at x = 7
What is +- 1/8 (plus or minus 1/8)
x(t) = 3sin(pi*t)
Is speed increasing or decreasing at time = 1.2 seconds?
What is decreasing?
d/dx[Integral(a=0,b=sin(x); 5t^2dt)]
5(sin(x))^2*cos(x)
Is there a a value on differentiable function f(x) where f'(x)=-3/2 between f(7)=9 and f(3) = 15?
What is by MVT, f'(x) = -3/2 exists on the given interval?
lim(x->2) (3-sqrt(x+7))/(x-2)
What is -1/6
d/dx arctan(5x)
What is 5/(1+25x^2)
v(t) = arctan(2x)
Is velocity increasing or decreasing at time = 1 sec?
Integral(a=0,b=2; 1/(x^2+10x+26) dx)
What is arctan(7)+arctan(5)
Is there a value of f(x) = 2x^2-3x+5 where f'(x) = 11 on the interval [2,5]?
What is by MVT, a value where f'(x)=11 exists between [2,5]?