h(x)=(7-4x)/(3+sqrt(9x-2)) We want to find lim_(x rarr3)h(x). What happens when we use direct substitution? Choose 1 answer: A The limit exists, and we found it! (B) The limit doesn't exist (probably an asymptote). (c) The result is indeterminate.

Plug x = 3: Let's try direct substitution by plugging x = 3 into h(x). h(3) = (7 - 4(3)) / (3 + sqrt(9(3) - 2))Simplify numerator and denominator: Simplify the numerator and the denominator. h(3) = (7 - 12) / (3 + sqrt(27 - 2))Continue simplifying: Continue simplifying. h(3) = (-5) / (3 + sqrt(25))Simplify square root: Simplify the square root. h(3) = (-5) / (3 + 5)Add numbers in denominator: Add the numbers in the denominator. h(3) = (-5) / 8Limit exists, answer is A: So, the limit exists and we found it by direct substitution. The answer is A The limit exists, and we found it!

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Let’s check out your problem:

h(x)=(7-4x)/(3+sqrt(9x-2))
We want to find
lim_(x rarr3)h(x).
What happens when we use direct substitution?
Choose 1 answer:
A The limit exists, and we found it!
(B) The limit doesn't exist (probably an asymptote).
(c) The result is indeterminate.

$h(x)=\frac{7-4 x}{3+\sqrt{9 x-2}}$ $\newline$ We want to find $\lim _{x \rightarrow 3} h(x)$ . $\newline$ What happens when we use direct substitution? $\newline$ Choose $1$ answer: $\newline$ (A) The limit exists, and we found it! $\newline$ (B) The limit doesn't exist (probably an asymptote). $\newline$ (C) The result is indeterminate.

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Math Problems

Algebra 1

Write and solve inverse variation equations

Full solution

h(x)=\frac{7-4 x}{3+\sqrt{9 x-2}}

\newline

We want to find

\lim _{x \rightarrow 3} h(x)

\newline

What happens when we use direct substitution?

\newline

Choose

1

answer:

\newline

(A) The limit exists, and we found it!

\newline

(B) The limit doesn't exist (probably an asymptote).

\newline

Plug $x = 3$ : Let's try direct substitution by plugging $x = 3$ into $h(x)$ . $\newline$ $h(3) = \frac{7 - 4(3)}{3 + \sqrt{9(3) - 2}}$
Simplify numerator and denominator: Simplify the numerator and the denominator. $h(3) = \frac{7 - 12}{3 + \sqrt{27 - 2}}$
Continue simplifying: Continue simplifying. $\newline$ $h(3) = \frac{-5}{3 + \sqrt{25}}$
Simplify square root: Simplify the square root. $h(3) = \frac{-5}{3 + 5}$
Add numbers in denominator: Add the numbers in the denominator. $\newline$ $h(3) = \frac{-5}{8}$
Limit exists, answer is $A$ : So, the limit exists and we found it by direct substitution. $\newline$ The answer is $A$ The limit exists, and we found it!