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

Show answers

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

10 glasses of juice could be made with 5 carrots, 1,500 orange juice, 2,000 papaya juice.

Answer from: Quest

answer: first option i.e. 'a' is correct.

step-by-step explanation:

since we have given that

number of minutes to wrap a small gift box = 4 minutes

we need to find the number of gifts to be wrapped in 5 minutes

since there is a direct variation, as the number of minutes will increase with number of gifts to be wrapped.

so, let the number of gifts to be wrapped in 5 minutes be x.

so, it becomes,

$\frac{1}{4}=\frac{x}{5}\\\\x=\frac{4}{5}\\\\x=0.8$

hence, first option 'a' is correct.

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

What is lim f(x)?
...