Limits
Evaluate
lim_{x\rightarrow9}x^2
What is 81?
Given f(x)=1/2x-2007 ,
d/dxf(x)
What is
1/2
Given f(x)=1/3e^(3x)
d/dxf(x)
What is
e^(3x)
The absolute maximum on the [0,2] interval for
f(x)=x^2
What is 4?
Evaluate
\int_0^{17}1\cdot dx
What is 17?
Evaluate
lim_{x\rightarrow\infty}(20x^4+2x^3-x^2+5x+20)/(5x^4-25)
What is 4?
Given f(x)=2sqrt(x) ,
d/dxf(x)
What is
1/sqrt(x)
Given xy=100 , we calculate this implicit derivative.
What is
y+xdy/dx=0
The absolute maximum on the (0,1] interval of
f(x)=1-3x
What is no absolute maximum exists?
Evaluate
\int_1^(e^3)1/xdx
What is 3?
Evaluate
lim_{x\rightarrow5}(x^2-25)/(x-5)
What is 10?
Given f(x)=-1/(2x^2) ,
d/dxf(x)
What is
1/x^3
Given f(x)=e^x-ln(x)
d/dxf(x)
What is
e^x-1/x
The critical values for the function
f(x)=|x-5|
What is 5?
Given \int_0^6f(x)dx=2\pi and \int_6^10f(x)dx=\pi , identify
\int_0^{10}f(x)dx
What is
3\pi
Given f(x)=x^2 , evaluate
\lim_{h\rightarrow0}(f(x+h)-f(x))/h
What is 2x?
Given f(x)=1/2x^2-4 and g(x)=1/3x^3-9
d/dx(f(x)\cdot g(x))
What is
x^3
Given y^3-y^2+1/2x^2=16 , we find this implicit derivative.
What is
3y^2dy/dx-2ydy/dx+x=0
Stationary points for the function
f(x)=100x-2x^2+144
What is 25?
Identify
d/dx(\int_a^xcos(t)dt)
What is cos(x)?
Evaluate
\lim_{h\rightarrow0}(e^h-1)/h
What is 1?
Given f(x)=(x-1)/x , evaluate
d/dxf(x)
What is
1/x^2
Given f(x)=5^(2x)-e^x ,
d/dxf(x)
What is
2\cdot ln(5)5^(2x)-e^x
A local minimum on the [0,10] interval for
f(x)=2.5x^2-10x+11
What is 1?
Evaluate
\int_0^1(4x+3)dx
What is 5?