contestada

If limit as x approaches a of f of x equals four and limit as x approaches a of g of x equals three, then limit as x approaches a of the quantity three times f of x squared minus four times g of x equals ten

true
false

Respuesta :

icedipping
False.

[tex] \lim_{x \to a} [3f(x)^{2} - 4g(x)] = 3[\lim_{x \to a}f(x)]^{2} - 4\lim_{x \to a}g(x) = 3(4)^{2} - 4(3) = 48 - 12 = 36[/tex]
abidemiokin

Since the result is not equal to 10 hence the expression [tex]\lim_{x \to a}[3f(x)^2-4g(x)]=10[/tex] is FALSE

  • Given the expression [tex]\lim_{x \to a}[3f(x)^2-4g(x)]=10[/tex]

  • We are to check if the expression is correct given that [tex]\lim_{x \to a} g(x) = 3 \ and \ \lim_{x \to a} f(x) = 4[/tex]

The limit above can be written as [tex]= 3\lim_{x \to a}[f(x)^2]-4[ \lim_{x \to a} g(x)]\\[/tex]

Substituting the given parameters

[tex]= 3\lim_{x \to a}[f(x)^2]-4[ \lim_{x \to a} g(x)]\\= 3(4)^2-4(3)\\=3(16) - 12\\=48-12\\=36[/tex]

Since the result is not equal to 10 hence the expression [tex]\lim_{x \to a}[3f(x)^2-4g(x)]=10[/tex] is FALSE

Learn more here: https://brainly.com/question/23935467

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