Domanda del libro di testo
Determine the following limits.
lim x→∞ 6x2/(4x^2+√(16x4 + x2))
388
views
Ch. 2 - Limits
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
TOC.tableOfContents
- Ch. 1 - Functions210
- Ch. 2 - Limits371
- Ch. 3 - Derivatives633
- Ch. 4 - Applications of the Derivative412
- Ch. 5 - Integration328
- Ch. 6 - Applications of Integration331
- Ch. 7 - Logarithmic, Exponential Functions, and Hyperbolic Functions177
- Ch. 8 - Integration Techniques394
- Ch. 9 - Differential Equations179
- Ch. 10 - Sequences and Infinite Series339
- Ch. 11 - Power Series218
- Ch.12 - Parametric and Polar Curves215
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243Non è quello che usi tu?Cambia libro di testo
Capitolo 2, Problema 31
Find the following limits or state that they do not exist. Assume a, b , c, and k are fixed real numbers.
lim x→2 (5x−6)^3/2
Guida verificata passo dopo passo1
Identify the type of limit problem: This is a direct substitution problem where we need to find the limit of a function as x approaches a specific value.
Recognize the function: The function given is \((5x - 6)^{3/2}\).
Apply direct substitution: Substitute \(x = 2\) into the function to evaluate the limit.
Calculate the expression inside the function: Compute \(5(2) - 6\) to simplify the expression inside the power.
Evaluate the power: Once the expression inside the function is simplified, raise it to the power of \(\frac{3}{2}\) to find the limit.
Risposta video verificata per un problema simile:
Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
1mConcetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Limits
A limit is a fundamental concept in calculus that describes the behavior of a function as its input approaches a certain value. It helps in understanding how functions behave near specific points, which is crucial for evaluating continuity and differentiability. In this case, we are interested in the limit of the function as x approaches 2.
Video consigliato:
05:50
One-Sided Limits
Continuous Functions
A function is continuous at a point if the limit of the function as it approaches that point equals the function's value at that point. For the limit to exist, the function must not have any breaks, jumps, or asymptotes at the point of interest. The expression (5x−6) is a polynomial, which is continuous everywhere, including at x = 2.
Video consigliato:
05:34Intro to Continuity
Evaluating Limits of Composite Functions
When evaluating limits of composite functions, such as (5x−6) raised to the power of 3/2, it is essential to first find the limit of the inner function before applying the outer function. This process often involves substituting the limit value into the inner function and then applying the outer function to that result, ensuring that the operations are valid within the domain of the functions involved.
Video consigliato:
3:48Evaluate Composite Functions - Special Cases
Pratica correlata
Domanda del libro di testo
Find the following limits or state that they do not exist. Assume a, b , c, and k are fixed real numbers.
lim x→1 x^2 − 1 / x − 1
266
views
Domanda del libro di testo
Determine whether the following statements are true and give an explanation or counterexample.
a. The value of does not exist.
363
views
Domanda del libro di testo
Determine the following limits.
lim x→3- x − 4 / x^2 − 3x
352
views
Domanda del libro di testo
Determine the following limits.
lim x→−∞ 40x^4+x^2+5x / √64x^8+x^6
379
views
1
rank
Domanda del libro di testo
Determine the following limits.
b. lim t→−2^− t^3 − 5t^2 + 6t / t^4 − 4t^2
336
views