Questions and Answers
What is the value of $\lim_{x \to 0} \frac{\ln(1+x)}{x}$?
1
What is the value of $\lim_{x \to \infty} \frac{x^2 + 3x - 2}{5x^2 + 3x}$?
1/5
If $P_n(x) = a_0x^n + a_1x^{n-1} + \ldots + a_n$, what is $\lim_{x \to a} P_n(x)$?
$P_n(a)$
What is $\lim_{x \to 0} \frac{\csc(x) - \cot(x)}{x}$?
Signup and view all the answers
What is $\lim_{x \to 1} \frac{x^3 - x}{x^2 - 1}$?
Signup and view all the answers
What is the limit of $\frac{x^2+1}{x^3+x}$ as $x$ approaches $0$?
Signup and view all the answers
What is the limit of $x ext{sin}(1/x)$ as $x$ approaches $0$?
Signup and view all the answers
What is the limit of $x^2 ext{cos}(1/x)$ as $x$ approaches $0$?
Signup and view all the answers
What is the limit of $(1+x)^{1/x}$ as $x$ approaches $0$?
Signup and view all the answers
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 $a$?
Signup and view all the answers
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.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
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.
