Limits
Evaluate
\lim_{x\rightarrow-1}|x|
What is 1?
Given a and b are constants, identify
d/dx(ax+b)
What is a?
The implicit derivative of
x^2+2xy=4
What is
2x+2y+2xdy/dx=0
The absolute maximum on the [0,1] interval for the function
-|x|
What is 0?
Where c is a constant real number, evaluate
\int_0^1cdx
What is c?
Evaluate
\lim_{x\rightarrow3}27/x
What is 9?
The slope of the tangent line to f(x)=3x^2+8 at x=2
What is 12?
d/dx(e^{1/3x}+e^2)
What is
1/3e^{1/3x}
The absolute minimum on the (0,1] interval for the function
f(x)=10-x
What is 9?
Where c is a constant, evaluate
\int_0^1c\cdot xdx
What is
c/2
Evaluate
lim_{x\rightarrow\infty}(5x^3-2x^2+x+23)/(20x^3-15
What is
1/4
d/dx(1/3x^3+1/2x^2-x+3)
What is
x^2+x-1
d/dx(x\cdot\ln(x))
What is
ln(x)+1
The absolute maximum on the interval [0,1] for the function
f(x)=x^2
What is 1?
Where c is a constant real number, evaluate
\int_1^ec/xdx
What is
c\cdot ln(x)]_1^e=c-0=c.
Evaluate
\lim_{x\rightarrow2}(x^2-4)/(x-2)
What is 4?
d/dx((3/2)/x^{2/3})
What is
-1/x^{5/3}
d/dx(e^{1/x})
What is
-1/x^2e^{1/x}
The local minimum on (0,1) of the function
f(x)=x+1
What is the local minimum does not exist.
Where c is a constant real number, evaluate
\int_0^1e^xdx
What is
e^1-1.
Evaluate
\lim_{h\rightarrow0}(1/(x+h)-1/x)/h
What is
-1/x^2
The slope of the normal line to the function f(x)=1/3x+18 at the point x=16.
What is -3?
d/dx(3^x-ln(x))
What is
ln(3)3^x-1/x
The stationary points for the function
f(x)=2x^3-24x
What are
x=\pm2
Given c is a real number, evaluate
\int_0^{1}3c\cdot x^2dx
What is
cx^3]_0^1=c.