Mathematics, 11.07.2021 22:40 SoccerHalo

Given f(x) = 3sqrt(2x-1).
6(2x-1)^2-3

What is lim f(x)?

Given f(x) = 3sqrt(2x-1).
6(2x-1)^2-3
What is lim f(x)?

Answers: 3

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Answers

Answer from: madisonwr

$\displaystyle 51$

General Formulas and Concepts:

Algebra I

Terms/CoefficientsFactoringFunctionsFunction Notation

Algebra II

Piecewise functions

Calculus

Limits

Right-Side Limit: $\displaystyle \lim_{x \to c^+} f(x)$

Limit Rule [Variable Direct Substitution]: $\displaystyle \lim_{x \to c} x = c$

Limit Property [Addition/Subtraction]: $\displaystyle \lim_{x \to c} [f(x) \pm g(x)] = \lim_{x \to c} f(x) \pm \lim_{x \to c} g(x)$

Limit Property [Multiplied Constant]: $\displaystyle \lim_{x \to c} bf(x) = b \lim_{x \to c} f(x)$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle f(x) = \left \{ {{3\sqrt{2x - 1}, \ x \leq 2} \atop {6(2x - 1)^2 - 3, \ x 2}} \right.$

Step 2: Solve

Substitute in function [Limit]: $\displaystyle \lim_{x \to 2^+} 6(2x - 1)^2 - 3$ Factor: $\displaystyle \lim_{x \to 2^+} 3[2(2x - 1)^2 - 1]$ Rewrite [Limit Property - Multiplied Constant]: $\displaystyle 3\lim_{x \to 2^+} 2(2x - 1)^2 - 1$ Evaluate [Limit Property - Variable Direct Substitution]: $\displaystyle 3[2(2 \cdot 2 - 1)^2 - 1]$ Simplify: $\displaystyle 51$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

Book: College Calculus 10e

Answer from: Quest

step-by-step explanation:

you can add the two numbers and divide the result by 2. or you can find the gap between the two numbers and add half of this to the smaller number.

Answer from: Quest

there are 70 more legs than eyes at the dog show (196 – 126 = 70). dogs have two more legs than eyes, and humans have the same number of legs as eyes. thus 70 is twice the number of dogs at the show, so the number of dogs is half of 70, which is 35. to get the number of humans, subtract 35 from 63: 63 – 35 = 28.

step-by-step explanation:

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Given f(x) = 3sqrt(2x-1).
6(2x-1)^2-3

What is lim f(x)?
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