Derivatives
d/dx(5x^2+3x)
What is
10x+3
When the denominator of y'=0 .
What is a vertical tangent?
If x(t)=sin^-1(t) , then v(t)=
What is
1/(sqrt(1-t^2)
lim_(x->a)f(x)=f(a)
What is the definition of continuity at a point?
Jump, cusp, corner, vertical tangent.
What are the points at which f'(x) DNE?
d/dx(cot^-1(5x))
What is
-5/(1+25x^2
The y coordinates when x=1 of 2xy^2-5xy=7
What are
y=1/7,-1?
y(t)=t^3-2t^2+7 . a(-2)=
What is
-16?
lim_(x->a)(f(x)-f(a))/(x-a)
What is the Alternate Definition of the Derivative?
lim_(x->-2)(x^3-5x+1)/(x^2-x-6)
What is DNE?
f(x)=x^2+5x , (f^-1)'(6)=
What is
1/7
The equation of the tangent line where y'=(3x^2y-1)/(x-10y^2) at the point (1,2) .
What is
y-2=(-5)/39(x-1)?
The time y=-16t^2+96t+10
reaches its maximum height.
What is
t=3?
lim_(h->0)(f(x+h)-f(x))/(h)
What is the limit definition of the derivative?
When lim_(x->a)f(x)=L but f(a)neL
What is a hole?
d/dx(log_7sec(x^3))
What is
(3x^2*tan(x^3))/(ln7)
If xy+cos(y)=3 , then y'(2,pi/2)=
What is
-pi/2
At t=a , v(a)>0 and a(a)<0 .
What is speed is, speed is decreasing is at
t=a?
If f is continuous on a closed interval [a,b] then f takes on all values between f(a) and f(b) .
What is the Intermediate Value Theorem?
lim_(x->0)(sin2x)/x
What is 2?
d/dx(cot^2(e^(4x)))
What is
-8cot(e^(4x))*csc^2(e^(4x))*e^(4x)?
If y^2=2x^2+y , then y''(1,2)=
What is
4/27
If v(t)=3t^2-17t+10 , the time t at which the particle ceases moving to the left.
What is
t=5
If lim_(x->infty)f(x)=b then y=b .
What is the definition of a horizontal asymptote?
lim_(h->0)(sin^-1(1/2+h)-pi/6)/h
What is
2/sqrt3