Basics to Learn

Question 1

derivative of cos

Answer 1

-sinx

Question 2

derivative of sin

Answer 2

cosx

Question 3

an integral of cos

Answer 3

sinx

Question 4

an integral of sin

Answer 4

-cosx

Question 5

sin(π/6)

Answer 5

1/2

Question 6

sin(π/4)

Answer 6

√2/2

Question 7

sin(π/3)

Answer 7

√3/2

Question 8

cos(π/6)

Answer 8

√3/2

Question 9

cos(π/4)

Answer 9

√2/2

Question 10

cos(π/3)

Answer 10

1/2

Question 11

tan(π/6)

Answer 11

√3/3

Question 12

tan(π/4)

Answer 12

1

Question 13

tan(π/3)

Answer 13

√3

Question 14

chain rule f(g(x))

Answer 14

g’(x) f’(g(x))

Question 15

product rule

Answer 15

(uv)’ = u’v + uv’

Question 16

Quotient rule

Answer 16

(u/v)’ = u’v - uv’ / v^2

Question 17

finding the area between two curves

Answer 17

∫ᵇₐ(function of top curve - function of bottom curve)dx

Question 18

integral of sec²x

Answer 18

tanx

Question 19

integral of eᵏˣ

Answer 19

1/keᵏˣ

Question 20

integral of 1/x

Answer 20

ln|x|

Question 21

integral of f’(x)/f(x)

Answer 21

ln|f(x)|+c

Question 22

sin cos identity

Answer 22

sin²x+cox²x=1

Question 23

sec tan identity

Answer 23

sec²x=1+tan²x

Question 24

cot cosec identity

Answer 24

1 + cot²x = cosec²x

Question 25

sin(2x)

Answer 25

2sin(x)cos(x)

Question 26

cos(2x) =

Answer 26

cos²x-sin²x

Question 27

tan(a+b)

Answer 27

tana+tanb/1-tanatanb

Question 28

y = f(x) + a

Answer 28

translates a in the y direction

Question 29

y = f(x+a)

Answer 29

translates -a in the x direction

Question 30

y = af(x)

Answer 30

stretch SF a in y direction

Question 31

y = f(ax)

Answer 31

stretch of 1/a in x direction

Question 32

y = -f(x)

Answer 32

reflection in x axis

Question 33

y = f(-x)

Answer 33

reflection in y axis

Question 34

limit as x tend to 0 of sinx/x

Answer 34

1

Question 35

limit as x tends to 0 of (1-cosx)/x²

Answer 35

1/2

Question 36

limit as x tends to infinity of (1+1/x)²

Answer 36

e

Question 37

limit as x tends to minus infinity of (1+1/x)²

Answer 37

e

Question 38

limit as x tends to 0 of (1+x)¹/ˣ

Answer 38

e

Question 39

limit as x tends to 0 of (log(1+x))/x

Answer 39

1

Question 40

limit as x tends to 0 of (eˣ-1)/x

Answer 40

1

Question 41

limit as x tends to infinity eˣ/xᵇ

Answer 41

infinity (for all b>0)

Question 42

limits as x tends to infinity logx/xᵇ

Answer 42

0

Question 43

limit as x tends to 0 from the right of xᵇlogx

Answer 43

0

Question 44

L’Hopitals Rule

Answer 44

Let a,b,c∈ℝ such that a≤b≤c and a!=b. Let Ω = (a,b){c}. Let f,g: Ω -> ℝ be differentiable functions such that g’(x)!=0 for all x∈Ω. Assume that one of the following conditions holds:

(i) limit as x tends to c of f(x) = 0 and limit as x tends to c of g(x) = 0
(ii) limits as x tends to c of f(x) = +- infinity and limit as x tends to c of g(x) = +- infinity