g(x)=(cos(x)-sin(x))/(cos(2x)) We want to find lim_(x rarr(pi)/(4))g(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.

Direct Substitution: First, let's try direct substitution of x = π/4 into the function g(x) to see what happens. g(π/4) = (cos(π/4) - sin(π/4)) / cos(2 * π/4)Calculate Trigonometric Values: Now, we calculate the values of cos(π/4), sin(π/4), and cos(2 * π/4). cos(π/4) = √2/2 sin(π/4) = √2/2 cos(2 * π/4) = cos(π/2) = 0Substitute Values into Function: Substitute these values into the function g(x). g(π/4) = (√2/2 - √2/2) / 0 This simplifies to: g(π/4) = 0 / 0Indeterminate Form: The result of the substitution is 0/0, which is an indeterminate form. This means that direct substitution does not give us the limit, and we need to apply other techniques to find the limit.

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g(x)=(cos(x)-sin(x))/(cos(2x))
We want to find
lim_(x rarr(pi)/(4))g(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.

$g(x)=\frac{\cos (x)-\sin (x)}{\cos (2 x)}$ $\newline$ We want to find $\lim _{x \rightarrow \frac{\pi}{4}} g(x)$ . $\newline$ 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 2

Solve a quadratic equation using the zero product property

Full solution

g(x)=\frac{\cos (x)-\sin (x)}{\cos (2 x)}

\newline

We want to find

\lim _{x \rightarrow \frac{\pi}{4}} g(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

Direct Substitution: First, let's try direct substitution of $x = \frac{\pi}{4}$ into the function $g(x)$ to see what happens. $\newline$ $g\left(\frac{\pi}{4}\right) = \frac{\cos\left(\frac{\pi}{4}\right) - \sin\left(\frac{\pi}{4}\right)}{\cos(2 \cdot \frac{\pi}{4})}$
Calculate Trigonometric Values: Now, we calculate the values of $\cos(\frac{\pi}{4})$ , $\sin(\frac{\pi}{4})$ , and $\cos(2 \times \frac{\pi}{4})$ . $\newline$ $\cos(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$ $\newline$ $\sin(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$ $\newline$ $\cos(2 \times \frac{\pi}{4}) = \cos(\frac{\pi}{2}) = 0$
Substitute Values into Function: Substitute these values into the function $g(x)$ . $g(\frac{\pi}{4}) = (\frac{\sqrt{2}}{2} - \frac{\sqrt{2}}{2}) / 0$ This simplifies to: $g(\frac{\pi}{4}) = \frac{0}{0}$
Indeterminate Form: The result of the substitution is $0/0$ , which is an indeterminate form. This means that direct substitution does not give us the limit, and we need to apply other techniques to find the limit.