Calculus 1 Exam 1 Terms

y = f(x) + c

Moves up

y = f(x) - c

Moves down

y = f(x+c)

Moves left

y = f(x-c)

Moves right

y = c * f(x)

Stretches vertically

y = (1/c) * f(x)

Shrinks vertically

y = f(c*x)

Shrinks horizontally

y = f(x/c)

Stretches horizontally

y = -f(x)

Flip over x-axis

y = f(-x)

Flip over y-axis

lim [f(x) - g(x)] = …?

lim f(x) - lim g(x)

lim [f(x) + g(x)] = …?

lim f(x) + lim g(x)

sin²x + cos²x =

1

1 + tan²x =

sec²x

1 + cot²x =

csc²x

sin (a+-b) =

sin(a)cos(b)+-cos(a)sin(b)

cos(a+-b) =

cos(a)cos(b)-+sin(a)sin(b)

sin(2x) =

2sin(x)cos(x)

cos(2x) =

cos²x-sin²x

lim (sin(x) / (x)) =

1

lim (tan(x) / (x)) =

1

lim (1-cos(x) / (x)) =

1

lim (1-cos(x) / (x²)) =

1/2

lim (sin(ax) / (x)) =

a

lim (tan(ax) / (x)) =

a