Find lim_(x rarr1)(sqrt(5x+4)-3)/(x-1). Choose 1 answer: (A) (3)/(5) (B) (5)/(6) (C) 1 (D) The limit doesn't exist

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Find  lim_(x rarr1)(sqrt(5x+4)-3)/(x-1). Choose 1 answer: (A)  (3)/(5) (B)  (5)/(6) (C) 1 (D) The limit doesn't exist

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Identify the form: Identify the form of the limit. We need to find the limit of the function (sqrt(5x+4)-3)/(x-1) as x approaches 1. Let's first substitute x with 1 to see if we can directly evaluate the limit. lim_(x -> 1)(sqrt(5x+4)-3)/(x-1) = (sqrt(5*1+4)-3)/(1-1) = (sqrt(9)-3)/0 = (3-3)/0 = 0/0 We get an indeterminate form 0/0, which means we need to apply a different method to evaluate the limit.Apply algebraic manipulation: Apply algebraic manipulation to simplify the expression. To resolve the indeterminate form, we can multiply the numerator and the denominator by the conjugate of the numerator. The conjugate of sqrt(5x+4)-3 is sqrt(5x+4)+3. lim_(x -> 1)((sqrt(5x+4)-3)(sqrt(5x+4)+3))/((x-1)(sqrt(5x+4)+3))Perform the multiplication: Perform the multiplication in the numerator. When we multiply the conjugate pairs in the numerator, we get a difference of squares, which simplifies to: (sqrt(5x+4))^2 - (3)^2 = (5x+4) - 9 = 5x - 5 The denominator remains as (x-1)(sqrt(5x+4)+3). lim_(x -> 1)((5x - 5))/((x-1)(sqrt(5x+4)+3))Simplify the expression further: Simplify the expression further. We notice that the numerator 5x - 5 can be factored out as 5(x - 1). This will allow us to cancel out the (x - 1) term in the denominator. lim_(x -> 1)(5(x - 1))/((x-1)(sqrt(5x+4)+3)) After canceling out the (x - 1) terms, we get: lim_(x -> 1)5/((sqrt(5x+4)+3))Evaluate the limit: Evaluate the limit of the simplified expression. Now that we have simplified the expression, we can directly substitute x with 1 to find the limit. lim_(x -> 1)5/((sqrt(5*1+4)+3)) = 5/((sqrt(9)+3)) = 5/((3+3)) = 5/6

Find $\lim _{x \rightarrow 1} \frac{\sqrt{5 x+4}-3}{x-1}$ . $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{3}{5}$ $\newline$ (B) $\frac{5}{6}$ $\newline$ (C) $1$ $\newline$ (D) The limit doesn't exist

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Find lim⁡x→15x+4−3x−1 \lim _{x \rightarrow 1} \frac{\sqrt{5 x+4}-3}{x-1} limx→1​x−15x+4​−3​.\newlineChoose 111 answer:\newline(A) 35 \frac{3}{5} 53​\newline(B) 56 \frac{5}{6} 65​\newline(C) 111\newline(D) The limit doesn't exist

Find $\lim _{x \rightarrow 1} \frac{\sqrt{5 x+4}-3}{x-1}$ . $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{3}{5}$ $\newline$ (B) $\frac{5}{6}$ $\newline$ (C) $1$ $\newline$ (D) The limit doesn't exist