Limits
Derivatives
Applications of Derivatives
Integrals
100
Find the limit
\lim_{x \to -3}\frac{x^2+7x+12}{x+3}
What is one
100
Find f'(x)
f(x)=3x^2-\sqrt{x}+\pisin(x)
What is
6x-\frac{1}{2\sqrt{x}}+\picos(x)
100
Find the critical values of f(x)
f(x)=\frac{1}{2}x^4-x^2+1
What are -1, 0, 1
100
Find the antiderivative
int2x^3+4x-7sin(x)dx
What is
\frac{1}{2}x^4+2x^2+7cos(x)+c
200
Find the limit
\lim_{z \to 1} \frac{\sqrt{5z+4} - 3}{z-1}
What is
\frac{5}{6}
200
Find the slope intercept equation of a tangent line of f(x) at x=1
f(x)=x e^x
What is
y=2ex-e
200
Find all points of inflection
f(x)=x^4-4x^3+6x^2-2
What are none
200
F(\frac{\pi}{4})=3
Find the particular solution
\int sec^2(x)dx
What is
tan(x)+2
300
Find the infinite limit
\lim_{x \to 0^-} \frac{\sqrt{x+1}}{2x}
What is
-\infty
300
find y', simplify fully
y=\frac{sin(x^2)}{x^2}
What is
\frac{2x^3cos(x^2)-2xsin(x^2)}{x^4}
300
on what intervals is sin(x) concave up on [-2𝝿, 2𝝿]
What is
(-pi,0) \cup(\pi, \2pi)
300
What is the total distance travelled by a particle following the velocity equation from t=0 to t=4
v(t)=t^2-3t
what is
\frac{19}{3}
400
Find the limit using LHopitals
\lim_{x \to \infty} \frac{ln(3t)}{t^2}
What is 0
400
Find the value c garunteed by the MVT on the interval [-1, 4] for
f(x)=2x^2-4x+1
What is
\frac{3}{2)
400
Find all relative extrema and their coordinate points
f(x)=\frac{-2}{x^2-4}
What is a relative min at (-0,1/2)
400
Solve the integral
\int \frac{sec(\frac{1}{x})}{x^2}dx
What is
-ln|sec(\frac{1}{x})+tan(\frac{1}{x})| + c
500
Is f(x) continuous at x=4, use the three part check for continuity, show full work
f(x)= 1, x \ge 0
f(x)=-1, x \lt 0
What is No
f(0)=1
\lim_{x \to 0}f(x) = D.N.E
500
A thin sheet of ice is in the form of a circle. If the ice is melting in such a way that the area of the sheet is decreasing at a rate of 0.5 m2/sec at what rate is the radius decreasing when the area of the sheet is 12 m2
What is −0.040717
500
What is wrong with this graph for a function f with the following properties
f is continuous over its domain, f'(-1) is undefined
f'(x)>0 on (-1,1), (5,8) f'(x)<0 on (-2,-1), (1,5)
f''(x)< 0 on (-2,-1) and f''(x)>0 on (-1,8)
f''(x)<0 on (-2,2)
f''(x)>0 on (2,8)
500
What is the average value of
f(x)=xe^{x^2}
over [0,3], round to three decimal places
what is 1350.347