Flashcard #1 Calculus

Describe the line and give the slope of:

y = 3

Horizontal

Slope is 0

What is the point-slope form of a linear equation

y - y₁ = m(x - x₁)

Describe the line and give the slope of:

x = 4

vertical line, undefined slope

What is the slope of any line that is perpendicular to the linear equation with slope m?

-1/m

What is the formula for finding the slope of a line?

m = delta y / delta x = (y2 - y1)/(x2 - x1) = (f(b) - f(a))/ b - a

Does the equation shown represent a function?

x^2 + y^2 = 4

No, this is a circle

If a function is odd then f(-x) = _______

-f(x)

If a function is even then f(-x)=___

f(x)

What is the domain of f(x) = x/x^2 - 1

x ≠ ± 1

The denominator of a rational function cannot equal zero

What is the domain of f(x) = ∛x + 1

All real numbers.

Any radical function with an odd index will have a domain of all real numbers.

Identify any horizontal and vertical asymptotes of f(x) = (3x + 1)/(2x^2 - 2)

y = 0

x = 1, -1

Identify any horizontal and vertical asymptotes of f(x) = (3x^2 + 1)/(4x^2 -16)

y = 3/4

x = 2, -2

Identify any horizontal and vertical asymptotes of f(x) = x^4 + 1 / x^2 + 4

none

Identify the domain of f(x) = x+1 / x^2 - 1

x ≠ ± 1

y = 3(2)^x is exponential ________

growth

y = (3/4)^x is exponential _________

decay

y = 4(2)^-x is exponential ___________

decay

y = (1/2)^-x is exponential __________

growth

Write 5^3 = 125 in logarithmic form

log5 125 = 3

Write log16 8 = 3/4 in exponential form

16^(3/4) = 8

What is the domain of log(x-4)

x > 4

What is the change of base formula?

logb (M) = loga (M)/loga (b)

Expand logb (MN)

= logb M + logb N

Expand logb (M/N)

= logb M - logb N

Expand logb (M^p)

=plogb M

Reciprocal Identities

sinθ = 1/cscθ ; cscθ = 1/sinθ

cosθ = 1/secθ ; secθ = 1/cosθ

tanθ = 1/cotθ ; cotθ = 1/tanθ

Quotient Identities

tanθ = sinθ/cosθ

cotθ = cosθ/sinθ

Even/Odd Identities

sin(-x) = - sin x

cos(-x) = cos x

tan (-x) = - tan x

csc (-x) = - csc x

sec (-x) = sec x

cot (-x) = - cot x

Pythagorean Identities

sin^2x+cos^2x=1

1+tan^2x=sec^2x

1+cot^2x=csc^2x

Distance formula

midpoint formula

Evaluate sin(0°)

0

Evaluate sin(π/6°)

1/2

Evaluate sin(π/4)

sqrt2/2

Evaluate sin(π/3)

sqrt3/2

Evaluate sin(π/2)

1

Evaluate sin(π)

0

Evaluate cos(0°)

1

Evaluate cos(π/6)

sqrt3/2

Evaluate cos(π/4)

√2/2

Evaluate cos(π/3)

1/2

Evaluate cot(π/2)

0

Evaluate cos(π)

-1

Evaluate tan(0)

0

Evaluate tan(π/6)

sqrt3/3

Evaluate tan(π/4)

1

Evaluate tan(π/3)

sqrt3

Evaluate tan(π/2)

undef

Evaluate tan(π)

0