Ms Howell Calculus 1+2

Limits

100

What is the limit as x approaches 0 of [sin(x)]/x

1

200

What is the limit as x approaches 0 of x/[sin(x)]

1

300

What is the limit as x approaches 0 of [1-cos(x)]/x

0

400

If a function has a hole, a jump, or a vertical asymptote, it is...

non-continuous

500

If f(c) exists, the limit as x approaches c exists, and if the limit of f(x) as x approaches c is equal to f(c). The function is...

continuous

Derivative Rules

100

What is the derivative of a constant

0

200

What is the derivative of mx+b

m

300

What is the derivative of xⁿ

nx^n-1

400

What is the derivative of f*g

f^I*g+f*g^I

500

What is the derivative of f/g

[f^I*g-f*g^I]/g²

Derivatives of Trigonometric Functions

100

What is the derivative of sin(x)

cos(x)

200

What is the derivative of cos(x)

-sin(x)

300

What is the derivative of tan(x)

sec²(x)

400

What is the derivative of cot(x)

-csc²(x)

500

What is the derivative of sec(x)

sec(x)tan(x)

Integral Rules

100

What letter is added to the end of every integral

C

200

What is the integral of 0

C

300

What is the integral of xⁿ

{[xⁿ⁺¹]/[n+1]}+C

400

What is the integral of k

kx+C

500

What is the integral of kx

k*[x²/2]

Integrals of Trigonometric Functions

100

What us the integral of cos(x)

sin(x)+C

200

What is the integral of sin(x)

-cos(x)+C

300

What is the integral of sec^2(x)

tan(x)+C

400

What is the integral of sec(x)tan(x)

sec(x)+C

500

What is the integral of csc^2(x)

-cot(x)+C