Unit 1 - Limits

Question 1

Limit of a function with constant value k

Answer 1

lim(k) as x—>c = k

Question 2

Limit of the identity function at x = c

Answer 2

lim(x) as x—>c = c

Question 3

Sum Rule of limits

Answer 3

lim (f(x) + g(x)) as x—>c = L + M

Question 4

Difference Rule of limits

Answer 4

lim (f(x) - g(x)) as x—>c = L - M

Question 5

Product Rule of limits

Answer 5

lim (f(x)g(x)) as x—>c = LM

Question 6

Constant Multiple Rule of limits

Answer 6

lim (kf(x)) as x —>c = kL

Question 7

Quotient Rule of limits

Answer 7

lim (f(x)/g(x)) as x—>c = L/M, M doesn’t equal 0

Question 8

Power Rule of limits

Answer 8

lim (f(x))^r/s as x—>c = L^r/s

Question 9

Limit of polynomial f(x)

Answer 9

f(c)

Question 10

Limit of the quotient of polynomials

Answer 10

lim (f(x)/g(x)) as x—>c = f(c)/g(c) where g(c) doesn’t equal 0

Question 11

Squeeze Theorem, where g(x) is less than or equal to f(x) which is less than or equal to h(x) for x+c is an interval about c

Answer 11

lim g(x) as x—>c = lim h(x) as x—>c = L, then lim f(x) as x—>c = L

Question 12

Limits describe…

Answer 12

How a function behaves as inputs approach a particular value

Question 13

How do limits as x—>c depend on how the function is defined at c?

Answer 13

They don’t

Question 14

Sum, difference, product, constant multiple, quotient, and power rules apply as limits approach infinity

Answer 14

True

Question 15

Horizontal asymptote

Answer 15

lim f(x) as x—>+-infinity = b

Question 16

Vertical asymptote

Answer 16

lim f(x) as x—> a^+ = +-infinity, or lim f(x) as x—>a^- = +-infinity

Question 17

Right end behaviour model

Answer 17

lim f(x)/g(x) as x—>infinity = 1

Question 18

Left end behaviour model

Answer 18

lim f(x)/g(x) as x—>-infinity = 1

Question 19

End behaviour model

Answer 19

Both a left and right end behaviour model

Question 20

The graph of a quotient will always have a vertical asymptote when the denominator equals 0

Answer 20

False

Question 21

End behaviour models can also model

Answer 21

horizontal asymptotes

Question 22

Continuous at a point c

Answer 22

lim f(x) as x—>c = f(c) OR
lim f(x) as x—>a^+ = f(a) or lim f(x) as x —>b^- = f(b)

Question 23

Composites of continuous functions are

Answer 23

continuous

Question 24

Algebraic combinations of continuous functions are

Answer 24

continuous

Question 25

3 step continuity test

Answer 25

(1) f(a) is defined
(2) lim f(x) as x—>a exists
(3) lim f(x) as x—>a = f(a)

Question 26

Slope of a line or derivative

Answer 26

m = lim as h—>0 of [f(a+h) - f(a)]/h

Question 27

Sensitivity (definition and equation)

Answer 27

how one variable responds to a small change in another variable
lim as x—>0 of delta(y)/delta(x)

Question 28

Secant line

Answer 28

goes through two points on a curve

Question 29

Average rate of a change can be thought of as

Answer 29

slope of a secant line

Question 30

Calculating tangent to a curve

Answer 30

(1) slope of a secant line through P and Q
(2) limit of secant slope as Q approaches P
(3) 2 = slope at P, tangent to curve at P is the line through P with this slope