MATH 20A Midterm 1

lim_x→0(sinx)/x

1

lim_x→0(1-cosx)/x

0

d/dx [sinx]

cosx

d/dx [cosx]

-sinx

d/dx [tanx]

sec²x

d/dx [secx]

secxtanx

d/dx [cscx]

-cscxcotx

d/dx [cotx]

-csc²x

d/dx [e^x]

e^x

d/dx [lnx]

1/x

d/dx [a^x]

a^xlna

d/dx [log_ax]

1/(x lna)

range of sin^-1x

[-π/2, π/2]

range of cos^-1x

[0, π]

range of tan^-1x

(-π/2, π/2)

range of cot^-1x

(0, π)

range of sec^-1x

[0, π/2)∩(π/2, π]

range of csc^-1x

[-π/2, 0)∩(0, π/2]