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Questions and Answers
What is the value of $\lim_{x \to 0} \frac{\ln(1+x)}{x}$?
What is the value of $\lim_{x \to \infty} \frac{x^2 + 3x - 2}{5x^2 + 3x}$?
If $P_n(x) = a_0x^n + a_1x^{n-1} + \ldots + a_n$, what is $\lim_{x \to a} P_n(x)$?
What is $\lim_{x \to 0} \frac{\csc(x) - \cot(x)}{x}$?
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What is $\lim_{x \to 1} \frac{x^3 - x}{x^2 - 1}$?
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What is the limit of $\frac{x^2+1}{x^3+x}$ as $x$ approaches $0$?
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What is the limit of $x ext{sin}(1/x)$ as $x$ approaches $0$?
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What is the limit of $x^2 ext{cos}(1/x)$ as $x$ approaches $0$?
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What is the limit of $(1+x)^{1/x}$ as $x$ approaches $0$?
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If $P_n(x) = a_0 + a_1x + a_2x^2 + ... + a_nx^n$, then what is the limit of $P_n(x)$ as $x$ approaches $a$?
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Study Notes
Limits of Functions
- The limit of ln(1+x)/x as x approaches 0 is 1.
- The limit of (x^2 + 3x - 2) / (5x^2 + 3x) as x approaches infinity is 1/5.
- The limit of P_n(x) = a_0x^n + a_1x^(n-1) + … + a_n as x approaches a is a_0a^n + a_1a^(n-1) + … + a_n.
- The limit of (csc(x) - cot(x)) / x as x approaches 0 is 0.
- The limit of (x^3 - x) / (x^2 - 1) as x approaches 1 is 3/2.
- The limit of (x^2 + 1) / (x^3 + x) as x approaches 0 is 1/0 = ∞.
- The limit of x sin(1/x) as x approaches 0 is 1.
- The limit of x^2 cos(1/x) as x approaches 0 is 0.
- The limit of (1+x)^(1/x) as x approaches 0 is e.
- The limit of P_n(x) = a_0 + a_1x + a_2x^2 + … + a_nx^n as x approaches a is a_0 + a_1a + a_2a^2 + … + a_na^n.
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Description
Test your understanding of calculus with this quiz on evaluating limits. Practice finding the limits of various functions and expressions, and sharpen your calculus skills.
