calc

Question 0

vertical tangent

Answer 0

discontinuity in which limits at a point go to same infinity

Question 1

cusp

Answer 1

discontinuity in which limits to a point go to opposite infinities

Question 2

deriv of sinx

Answer 2

cosx

Question 3

deriv of cosx

Answer 3

-sinx

Question 4

deriv of tanx

Answer 4

sec^2x

Question 5

deriv of cscx

Answer 5

-cscxcotx

Question 6

deriv of secx

Answer 6

secxtanx

Question 7

deriv of cotx

Answer 7

-csc^2x

Question 8

deriv of lnx

Answer 8

1/x

Question 9

deriv of logax

Answer 9

1/x • 1/lna

Question 10

deriv of e^x

Answer 10

e^x

Question 11

deriv of a^x

Answer 11

a^x • lna

Question 12

when first deriv changes from positive to negative

Answer 12

local max

Question 13

when first deriv changes from negative to positive

Answer 13

local min

Question 14

when first deriv = 0 and the second deriv is negative

Answer 14

local max

Question 15

when first deriv = 0 and second deriv is positive

Answer 15

local min

Question 16

positive f’(x)

Answer 16

f is increasing

Question 17

negative f’(x)

Answer 17

f is decreasing

Question 18

f’(x) increasing

Answer 18

second deriv is positive, f is concave up

Question 19

f’(x) decreasing

Answer 19

second deriv is negative, f is concave down

Question 20

trapezoid rule

Answer 20

1/2🔺x (f(x0) + 2f(x1)…. + f(xn))

Question 21

dy/dx = ky

Answer 21

y = Ce^kx

Question 22

newtons law of cooling

Answer 22

T = Ce^kt + Ts

Question 23

dP/dt = kP(m-P)

Answer 23

P(t) = m/ 1+ Ce^-mkt

Question 24

how to find position at a particular time given velocity

Answer 24

use FTC | integral of velocity = s(b) - s(a)

Question 25

to find total distance traveled

Answer 25

absolute value of velocity in an integral

Question 26

finding areas of the plane with respect to x

Answer 26

integrate from left to right, the top function minus the bottom function

Question 27

areas in the plane with respect to y

Answer 27

integrate from bottom to top the right function minus the left function