Question

Evaluate Lim
12x + 3
x3
x + 3​

Answer 1

the following limits. x→-2 x^3 + x^2 + 4x + 12x^3 - 3x + 2 .

Click here to get an answer to your question ✍️ Evaluate the following limits. x→-2 x^3 + x ^2 + 4x + 12x^3 - 3x + 2 .

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Answer 2

EXPLANATION.

$\sf \implies \lim_{x \to 3} \dfrac{\sqrt{2x+3} }{x + 3}$

As we know that,

If limit is not come in indeterminate form, then just evaluate the equation and put the values.

Put x = 3 in equation, we get.

$\sf \implies \lim_{x \to 3} \dfrac{\sqrt{2x + 3} }{x + 3}$

$\sf \implies \lim_{x \to 3} \dfrac{\sqrt{2(3)+3} }{3 + 3}$

$\sf \implies \lim_{x \to 3}\dfrac{\sqrt{6 + 3} }{6}$

$\sf \implies \lim_{x \to 3}\dfrac{\sqrt{9} }{6}$

$\sf \implies \lim_{x \to 3} \dfrac{3}{6} = \dfrac{1}{2}$

                                                                                                                       

MORE INFORMATION.

Indeterminate form.

(1) = 0 x ∞.

(2) = 0°.

(3) = $1^{\infty}$

(4) = ∞ - ∞.

(5) = ∞/∞.

(6) = ∞°.

(7) = 0/0.

Limits of a function.

$\sf \implies \lim_{x \to a}f(x) = l$

For finding right hand limit of a function we write (x + h) in place of x while for left hand limit we write (x - h) in place of x.