Calc 213

Question 1

d/dx sinx

Answer 1

cosx

Question 2

d/dx cosx

Answer 2

-sinx

Question 3

d/dx tanx

Answer 3

sec²x

Question 4

d/dx cotx

Answer 4

• csc²x

Question 5

d/dx sec x

Answer 5

sec x tan x

Question 6

d/dx csc x

Answer 6

-csc x cot x

Question 7

∫ sin x dx

Answer 7

• cos x + C

Question 8

∫ cos x dx

Answer 8

sin x + C

Question 9

∫ sec² x dx

Answer 9

tan x + C

Question 10

∫ csc² x dx

Answer 10

• cot x + C

Question 11

∫sec x tan x dx

Answer 11

sec x + C

Question 12

∫csc x cot x dx

Answer 12

• csc x + C

Question 13

lim _{x -> a} [f(x) +/- g(x)]

Answer 13

lim _{x -> a} f(x) +/- lim _{x -> a} g(x)

Question 14

lim _{x -> a} [f(x) * g(x)]

Answer 14

lim _{x -> a} f(x) * lim _{x -> a} g(x)

Question 15

lim x -> a p(x)

(p = polynomial)

Answer 15

p(a)

Question 16

If f(x) = g(x)

Answer 16

the limits of the functions are equal for all when “x” does not equal “a”

Question 17

d/dx [a^g(x)]

Answer 17

(ln a)*a^g(x)*g’(x)

Question 18

Trapezoidal Rule

Answer 18

∫_a^bf(x) dx ≈ ((b-a)/n) [1/2 f(x₀) + f(x₁)… + 1/2f(x_n)]

Question 19

Simpson’s Rule

Answer 19

∫_a^bf(x) dx ≈

((b-a)/3n) [f(x₀) +4f(x₁)+ 2f(x₂) … + f(x_n)]

Question 20

∫ u dv

Answer 20

uv - ∫ v du