Limits
\lim_{x\to 2} \frac{x^2-4}{x-2}
What is 4
if f'(x)>0, what does that imply for the function f?
When does a vertical asymptote occur
What is when the denominator=0
When can you use L'hopitals rule
What is 0/0 or
\infty/\infty
What does
\int_a^bf(x) dx
represent
what is Net area
\lim_{x\to0} \frac{sin(x)}x
What is 1
\frac{d}{dx} (x^3-3x)
What is
3x^2-3
Find the horizontal asymptotes:
f(x)=\frac{2x+1}{x}
What is y=2
Evaluate:
\lim_{x\to\infty} ln(x)/x
What is 0
Evaluate
\int_0^2 x \ dx
What is 2
\lim_{x\to\infty} \frac{3x^2+1}{x^2-5}
What is 3
Find the critical points of:
f(x)=x^3-3x
What is x=+-1
What is the intervals of increasing:
f'(x)=x(x-2)
What is
(-\infty,0)\cup(2,\infty)
\lim_{x\to0} (1+x)^{1/x}
What is e
Evaluate
\int_2^4(3x^2)dx
what is 56
Find all discontinuities:
f(x)=\frac{x^2-9}{x-3}
What is removable at x=3
f(x)=x^3-3x
Given that x=1 is a critical point, use the second derivative test to determine if it is a minimum, maximum, or neither:
What is x=0
Determine concavity if
f''(x)>0
What is concave up
What dimensions maximize the area of a rectangle with perimeter 20.
What is 5x5
Find the total distance traveled by a particle, given the velocity function from 0 to 3
v(t)=4-2t
What is 5
\lim_{x\to0} \frac{1-cos(x)}{x^2}
What is 1/2
Find inflection points for:
f(x)=2x^4-3x^2+2
x=+-1/2
Where are the vertical asymptotes:
f(x)=\frac{x}{x-1}
What is x=1
Maximize the product with the constraint function (what x,y values):
x+y=10
what is x=5,y=5
Find this derivative:
\frac{d}{dx} int_0^{2x}(t^2+1)dt
What is 8x^2+2