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Questions and Answers
In Lab activity 1.2.4, what function is used to find the difference quotient?
In Lab activity 1.2.4, what function is used to find the difference quotient?
- $f(x) = x$
- $f(x) = x^3$
- $f(x) = x^4$
- $f(x) = x^2$ (correct)
Which limit expression is used in Lab activity 2.3.4?
Which limit expression is used in Lab activity 2.3.4?
- $\lim_{h \to 0} \frac{f(a+h) - f(a)}{h^2}$
- $\lim_{h \to \infty} \frac{f(a+h) - f(a)}{h}$
- $\lim_{a \to 0} \frac{f(a+h) - f(a)}{h}$
- $\lim_{h \to 0} \frac{f(a+h) - f(a)}{h}$ (correct)
During the differentiation proof in Lab activity 2.3.4, which algebraic identity is used for rationalizing the denominator?
During the differentiation proof in Lab activity 2.3.4, which algebraic identity is used for rationalizing the denominator?
- $a^2 + b^2 = (a+b)^2$
- $a^2 - 2ab + b^2 = (a-b)^2$
- $a^2 + 2ab + b^2 = (a+b)^2$
- $a^2 - b^2 = (a-b)(a+b)$ (correct)
In Lab activity 2.3.4, given $f(x) = \sqrt{x}$, which expression represents $f(a+h)$?
In Lab activity 2.3.4, given $f(x) = \sqrt{x}$, which expression represents $f(a+h)$?
In the differentiation process shown, what final expression is obtained for $\frac{d}{dx} \sqrt{x}$?
In the differentiation process shown, what final expression is obtained for $\frac{d}{dx} \sqrt{x}$?
Flashcards
Difference quotient formula
Difference quotient formula
Used to calculate the instantaneous rate of change of a function. The formula is: (f(a+h) - f(a)) / h, as h approaches 0.
Limit expression for derivative
Limit expression for derivative
Represents the instantaneous rate of change of a function at a specific point. It is written as the limit of (f(a + h) - f(a)) / h as h approaches 0.
Algebraic identity for rationalizing denominator
Algebraic identity for rationalizing denominator
a² - b² = (a-b)(a+b) is used to simplify expressions with square roots in denominators by multiplying by the conjugate
f(a+h) for f(x)=√x
f(a+h) for f(x)=√x
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Derivative of √x
Derivative of √x
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