Find lim_(x rarr-4)(7x+28)/(x^(2)+x-12) Choose 1 answer: (A) 1 (B) 7 (c) -1 (D) The limit doesn't exist

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Find  lim_(x rarr-4)(7x+28)/(x^(2)+x-12) Choose 1 answer: (A) 1 (B) 7 (c) -1 (D) The limit doesn't exist

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Substitute and Evaluate: First, let's try to directly substitute the value of x with -4 into the function to see if it results in an indeterminate form or not. Substitute x = -4 into (7x+28)/(x^2+x-12).  lim_(x rarr-4)(7x+28)/(x^2+x-12) = (7(-4)+28)/((-4)^2+(-4)-12) = (-28+28)/(16-4-12) = 0/0  Since we get 0/0, which is an indeterminate form, we cannot directly evaluate the limit by substitution.Factorize Denominator: Next, we should try to factor the numerator and the denominator to see if there are any common factors that can be canceled out. Factor the quadratic expression in the denominator x^2 + x - 12.  x^2 + x - 12 can be factored into (x + 4)(x - 3).  Now, let's rewrite the limit expression with the factored form of the denominator.  lim_(x rarr-4)(7x+28)/((x + 4)(x - 3))Factorize Numerator: Notice that the numerator 7x + 28 can also be factored because it is a common factor of 7.  Factor out the common factor of 7 from the numerator.  7x + 28 can be factored into 7(x + 4).  Now, let's rewrite the limit expression with the factored form of the numerator.  lim_(x rarr-4)(7(x + 4))/((x + 4)(x - 3))Cancel Common Factor: We can now cancel out the common factor (x + 4) from the numerator and the denominator, as long as x is not equal to -4. Since we are taking the limit as x approaches -4, not at x = -4, we can cancel the factors.  Cancel the (x + 4) term from the numerator and the denominator.  lim_(x rarr-4)7/(x - 3)Final Substitution: Now that we have a simplified expression, we can substitute x = -4 into the limit to find the value.  Substitute x = -4 into 7/(x - 3).  lim_(x rarr-4)7/(x - 3) = 7/((-4) - 3) = 7/(-7) = -1  The limit exists and is equal to -1.

Find $\lim _{x \rightarrow-4} \frac{7 x+28}{x^{2}+x-12}$ . $\newline$ Choose $1$ answer: $\newline$ (A) $1$ $\newline$ (B) $7$ $\newline$ (C) $-1$ $\newline$ (D) The limit doesn't exist

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Find $\lim _{x \rightarrow-4} \frac{7 x+28}{x^{2}+x-12}$ . $\newline$ Choose $1$ answer: $\newline$ (A) $1$ $\newline$ (B) $7$ $\newline$ (C) $-1$ $\newline$ (D) The limit doesn't exist