Find the limit
limx->-1 (x2 + x - 6) =
limx->-1 (x2 + x - 6) = (-1)2 + (-1) - 6
= -6
limx->-1(x2 + x - 6) / (x + 3) =
limx->-1(x2 + x - 6) / (x + 3) =
[(-1)2 + (-1) - 6] / (-1 + 3) = -6/2 = -3
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: limx->infinity(3x6 - 7x2 + 2x)/(5x6 + 8) = 3/5
Hangman: Math word
_ _ _ _ _ _ _ _ _ _ _
PRECALCULUS
limx->2(x2 - 4) / (x - 2)
limx->2(x2 - 4) / (x - 2)
(22 - 4) / (2 - 2) = 0/0 -> Nope
(x + 2)(x - 2) / (x - 2) = x + 2
limx->2(x+2) = 4
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: limx->infinity(2x2 + 4x - 5) / (x6 - 4x3 + 5) = 0
How do you calculate BMI?
How do you calculate BMI?
BMI = weight (kg) / height (m)2
limx->0(sqrt(x+1) - 1) / x
limx->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
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)
Hangman: Chinese city
_ _ _ _
NEHE
limx->0((sin(x) - 1) / x3)
limx->0((sin(x) - 1) / x3) = -1/6