G9 Math Midterm Review

Find the limit

100

lim_x->-1 (x² + x - 6) = 

lim_x->-1 (x² + x - 6) = (-1)² + (-1) - 6

= -6

200

lim_x->-1(x² + x - 6) / (x + 3) =

lim_x->-1(x² + x - 6) / (x + 3) =

[(-1)² + (-1) - 6] / (-1 + 3) = -6/2 = -3

300

lim_x->2(x² - 4) / (x - 2)

lim_x->2(x² - 4) / (x - 2)

(2² - 4) / (2 - 2) = 0/0 -> Nope

(x + 2)(x - 2) / (x - 2) = x + 2

lim_x->2(x+2) = 4

400

lim_x->0(sqrt(x+1) - 1) / x

lim_x->0(sqrt(x+1) - 1) / x

Direct substitution -> 0/0 

Rationalizing numerator -> [(x+1) - 1] / [x(sqrt(x + 1)) + 1]

Simplify: 1 / [sqrt(x + 1) + 1]

Plug in x=0: 1/[sqrt(0+1) + 1] = 1/2

500

lim_x->0((sin(x) - 1) / x³)

lim_x->0((sin(x) - 1) / x³) = -1/6

(Blank)

200

Recall that a rational function is a function where R(x) = p(x)/q(x), where p(x) and q(x) are both polynomials.

What is the limit as R(x) approaches infinity when p(x) and q(x) have the same leading power?

Recall that a rational function is a function where R(x) = p(x)/q(x), where p(x) and q(x) are both polynomials.

What is the limit as R(x) approaches infinity when p(x) and q(x) have the same leading power? The ratio of the leading coefficients

Ex: lim_x->infinity(3x⁶ - 7x² + 2x)/(5x⁶ + 8) = 3/5

300

Recall that a rational function is a function where R(x) = p(x)/q(x), where p(x) and q(x) are both polynomials.

What is the limit as x approaches infinity of a rational function where the leading power of q(x) is greater than the leading power of p(x)?

Recall that a rational function is a function where R(x) = p(x)/q(x), where p(x) and q(x) are both polynomials.

What is the limit as x approaches infinity of a rational function where the leading power of q(x) is greater than the leading power of p(x)? 0

example: lim_x->infinity(2x² + 4x - 5) / (x⁶ - 4x³ + 5) = 0

400

If the graph of a function has a vertical asymptote, the limit of that function as x approaches the value where the asymptote exists is...

If the graph of a function has a vertical asymptote, the limit of that function as x approaches the value where the asymptote exists is...undefined 

(positive or negative infinity, which also means undefined)

Random

200

Hangman: Math word

_ _ _ _ _ _ _ _ _ _ _

PRECALCULUS

300

How do you calculate BMI?

How do you calculate BMI?

BMI = weight (kg) / height (m)²

400

Hangman: Chinese city

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NEHE