Midterm 2

Question 1

d/dx(arcsin(x))

Answer 1

1/(sqrt(1-x**2))

Question 2

d/dx(arccos(x))

Answer 2

-(1/(sqrt(1-x**2)))

Question 3

d/dx(arctan(x))

Answer 3

1/(1+x**2)

Question 4

d/dx(arccot(x))

Answer 4

-(1/(1+x**2))

Question 5

d/dx(arcsec(x))

Answer 5

1/(|x|sqrt(x**2-1))

Question 6

d/dx(arccsc(x))

Answer 6

-(1/(|x|sqrt(x**2-1)))

Question 7

d/dx(sin(x))

Answer 7

cosx

Question 8

d/dx(cos(x))

Answer 8

-sin(x)

Question 9

d/dx(tan(x)

Answer 9

(sec(x))**2

Question 10

d/dx(cot(x))

Answer 10

-(csc(x))**2

Question 11

d/dx(sec(x))

Answer 11

sec(x)tan(x)

Question 12

d/dx(csc(x))

Answer 12

-csc(x)cot(x)

Question 13

(sinx)2+(cosx)2

Answer 13

1

Question 14

sin(x+y)

Answer 14

sinxcosy+cosxsiny

Question 15

sin(x-y)

Answer 15

sinxcosy-cosxsiny

Question 16

cos(x+y)

Answer 16

cosxcosy-sinxsiny

Question 17

cos(x-y)

Answer 17

cosxcosy+sinxsiny

Question 18

sin(2x)

Answer 18

2sinxcosx

Question 19

cos(2x)

Answer 19

cosx2-sinx2
2cosx2-1
1-2(sinx2)

Question 20

lim(sinx/x) (x goes to 0)

Answer 20

1

Question 21

lim((1-cosx)/x) (x goes to 0)

Answer 21

0

Question 22

limit that goes to 1

Answer 22

lim(sinx/x) (x goes to 0)

Question 23

limit that goes to 0

Answer 23

lim((1-cosx)/x) (x goes to 0)

Question 24

Cylinder

Answer 24

A = 2(pi)r**2+2(pi)rh
V = (pi)(r**2)h

Question 25

Sphere

Answer 25

A = 4(pi)r**2
V = (4/3)(pi)r**3

Question 26

Cone

Answer 26

A = (pi)rs + (pi)r**2
s = side (angled height)
V = (1/3)(pi)(r**2)h

Question 27

Square- Based Pyramid

Answer 27

A = (1/2)bs(4)+(b**2)
V = (1/3)(b**2)h