Limits
Derivatives
Integrals
Exponential and Logs
Random
100
Does the Limit exist when x approaches zero of the function f(x)=((x^2+3)/x)?
Limit does exist.
100
What is the Power Rule?
(x^n)d/dx=nx^(n-1)
100
What is the anti derivative of f(x) if f(x)=x?
((x^2)/2)+C
100
What is the limit if x approaches negative infinity of f(x) if f(x)=e^x?
0
100
The special trig limits are... The ones you needed to memorize before learning about L'Hopital's Rule!
sin (x)/x = 1 1-cos(x)/x = 0
200
Does the Limit exist as x approaches zero of √(x)?
No, it does not exist because the limit when approaching on the left does not exist.
200
What is the derivative of arcsinx?
1/(√(1-x^2))
200
What is the difference between anti derivatives different from indefinite integrals?
Nothing they mean the same thing.
200
What is the derivative of f(x) if f(x)=2^(-3x)?
(ln2)(-3)2^(-3x)
200
What is the three step definition of continuity?
1. The function is defined at a point. 2. The function has a limit as it approaches the point. 3. The limit and the function at the point are the same.
300
Does the limit exist as x approaches zero (FROM BOTH SIDES) of the function f(x)=lnx?
Does not exist, Using L'Hopitals Rule the limit exists on the right side but does not exist on the left side.
300
What is the definition/formula of a derivative?
f(x)d/dx= lim as h->0 of [f(x+h)-f(x)]/h or lim as x->a of[f(x)-f(a)]/[x-a]
300
What is the anti derivative of of (sec^2(3x))?
(tan3x)/3 +C
300
What is another way of writing ln(x/y)?
lnx-lny
300
What is Rolles Theorem?
f(a)=f(b) and f(x) is continuous then f'(p)=0 and a<p<b
400
What is the left hand limit as x approaches zero of the function f(x)=cot(x)?
negative infinity.
400
find the derivative with respect to x of y^2 +x^2=9
y'=-x/y
400
What is the formula of the power rule when used with anti derivatives?
F(x)=(x^(n+1))/(n+1) +C
400
What is the derivative with respect to x of ln(x/y)?
1/x
400

Specify 4 types of functions that are continuous?

What is Varying, Trig, Polynomial, Exponential, Logarithmic, Linear?

500
What is the limit as x approaches infinity of f(x), if f(x)=arctanx?
1.
500

What is the derivative of arctan(x/6)?

6/(x^2+36)

500
what is the anti derivative of (2sinxcosx)?
-cos2x/2 +C
500
what is the limit of f(x) as x approaches 0 if f(x)=sin(lnx)
DNE
500

Name 5 mathematicians that contributed greatly to calculus?

What is Newton, Leibeniz, Reimann, L'hospital, Rolles, James Gregory, Maclaurin, Bonaventura Cavalieri,  Maria Gaetana Agnesi?

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