Find lim_(x rarr3)(x-3)/(sqrt(4x+4)-4). Choose 1 answer: (A) -4 (B) 1 (C) 2 (D) The limit doesn't exist

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Find  lim_(x rarr3)(x-3)/(sqrt(4x+4)-4). Choose 1 answer: (A) -4 (B) 1 (C) 2 (D) The limit doesn't exist

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Identify Indeterminate Form: Identify the indeterminate form. We need to evaluate the limit of the function (x-3)/(sqrt(4x+4)-4) as x approaches 3. Let's first plug in the value of x = 3 to see if the function is defined at that point or if it results in an indeterminate form. lim_(x -> 3)(x-3)/(sqrt(4x+4)-4) = (3-3)/(sqrt(4*3+4)-4) = 0/0 This is an indeterminate form, so we cannot directly evaluate the limit.Rationalize Denominator: Rationalize the denominator. To resolve the indeterminate form, we can multiply the numerator and the denominator by the conjugate of the denominator. The conjugate of sqrt(4x+4)-4 is sqrt(4x+4)+4. lim_(x -> 3)((x-3)(sqrt(4x+4)+4))/((sqrt(4x+4)-4)(sqrt(4x+4)+4))Apply Difference of Squares: Apply the difference of squares formula. When we multiply the denominator by its conjugate, we get a difference of squares, which simplifies to: (sqrt(4x+4)-4)(sqrt(4x+4)+4) = (sqrt(4x+4))^2 - (4)^2 = 4x+4 - 16 = 4x - 12Simplify Expression: Simplify the expression. Now we simplify the numerator and the denominator separately: Numerator: (x-3)(sqrt(4x+4)+4) Denominator: 4x - 12 The limit becomes: lim_(x -> 3)((x-3)(sqrt(4x+4)+4))/(4x - 12)Factor Out Common Term: Factor out the common term in the denominator. We notice that the denominator 4x - 12 can be factored out as 4(x - 3). This will allow us to cancel out the (x-3) term in the numerator and the denominator. lim_(x -> 3)((x-3)(sqrt(4x+4)+4))/(4(x - 3))Cancel Common Terms: Cancel out the common terms. After factoring, we can cancel the (x-3) term in the numerator and the denominator: lim_(x -> 3)(sqrt(4x+4)+4)/4Plug in Value: Plug in the value of x = 3. Now that we have simplified the expression and eliminated the indeterminate form, we can safely substitute x = 3 into the limit: lim_(x -> 3)(sqrt(4*3+4)+4)/4 = (sqrt(12+4)+4)/4 = (sqrt(16)+4)/4 = (4+4)/4 = 8/4 = 2

Find $\lim _{x \rightarrow 3} \frac{x-3}{\sqrt{4 x+4}-4}$ . $\newline$ Choose $1$ answer: $\newline$ (A) $-4$ $\newline$ (B) $1$ $\newline$ (C) $2$ $\newline$ (D) The limit doesn't exist

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Find lim⁡x→3x−34x+4−4 \lim _{x \rightarrow 3} \frac{x-3}{\sqrt{4 x+4}-4} limx→3​4x+4​−4x−3​.\newlineChoose 111 answer:\newline(A) −4-4−4\newline(B) 111\newline(C) 222\newline(D) The limit doesn't exist

Find $\lim _{x \rightarrow 3} \frac{x-3}{\sqrt{4 x+4}-4}$ . $\newline$ Choose $1$ answer: $\newline$ (A) $-4$ $\newline$ (B) $1$ $\newline$ (C) $2$ $\newline$ (D) The limit doesn't exist