Podcast
Questions and Answers
Simplify the expression: 1/(x - 1) + 1/(x^2 - 1)
Simplify the expression: 1/(x - 1) + 1/(x^2 - 1)
(x + 2)/(x^2 - 1)
Simplify the expression: (x^2 - 1)/(x^2 - 2x + 1)
Simplify the expression: (x^2 - 1)/(x^2 - 2x + 1)
(x + 1)/(x - 1)
Simplify the expression: x/(x^2 - 1)
Simplify the expression: x/(x^2 - 1)
x/((x + 1)(x - 1))
Evaluate the limit as x approaches 1 of (x^2 - 1)/(x - 1)
Evaluate the limit as x approaches 1 of (x^2 - 1)/(x - 1)
Flashcards
h(t) = t + 1/t
h(t) = t + 1/t
A function where 't' is added to its reciprocal.
h(-1)
h(-1)
The value of the function h(t) when t = -1.
h(2)
h(2)
The value of the function h(t) for t = 2.
g(t) = t + 2 / (t - 2)
g(t) = t + 2 / (t - 2)
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g(0)
g(0)
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g(a)
g(a)
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Undefined g(t)
Undefined g(t)
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g(2)
g(2)
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function evaluation
function evaluation
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h(x-1)
h(x-1)
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Study Notes
Homework 24
- Function h(t): A function is defined with a formula, h(t) = t/2 + 1/2 + 1/t.
- Values of h(t):
- h(-1) = -1/2 + 1/2 + (-1) = -1
- h(2) = 2/2 + 1/2 + 1/2 = 2
- h(1/2) = 1/4 + 1/2 + 2 = 9/4 = 2.25
- h(x-1) = (x-1)/2 + 1/2 + 1/(x-1).
- h(π) = π/2 + 1/2 + 1/π
Function g(t):
- Function g(t): Definition: g(t) = t+2 / t-2
- Values of g(t):
- g(-2) = -2+2 / -2-2 = 0/-4 = 0
- g(2) = 2+2 / 2-2 = 4/0, Undefined
- g(0) = 0+2 / 0-2 = 2/-2 = -1
- g(a) = a+2 / a-2
- g(a²-2) = (a²-2)+2 / (a²-2)-2 = a² / a²-4
- g(a+1) = (a+1) + 2 / (a+1) - 2 = a+3 / a-1
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Description
This quiz explores the functions h(t) and g(t), providing specific values and calculations for each function. It includes the evaluation of various inputs into the functions, revealing their behavior and properties. Test your understanding of these mathematical functions and their applications.
